Hexagon Formula: Geometry deals with the study of various shapes. Derivation. The ratio between the number of sides of two regular polygon 1 : 2 and the ratio between their . To solve more problems on the topic, download BYJU’S-The Learning App. A regular hexagon has a total number of 9 diagonals. We know that the area of an equilateral triangle is \(\frac{{\sqrt 3 {a^2}}}{4}\,{\rm{square}}\,{\rm{units}},\) where \(a\) is the side length of the equilateral triangle.Hence, we can calculate the area of the hexagon if we combine six such triangles, which is \(6 \times \frac{{\sqrt 3 {a^2}}}{4} = \frac{{3\sqrt 3 {a^2}}}{2}{\text{square}}\,{\text{units}}.\), Q.1. If you know the length of one of the sides, the apothem length is given by the formula: where: |. A regular hexagon is one that has all of its sides equal and all of its angles congruent. If we know the area of one equilateral triangle, we can easily calculate the area of the hexagon. In order to calculate the area of a hexagon, we divide it into small six isosceles triangles. Hexa is a Greek word whose meaning is six. 2 We can have regular and irregular hexagons. An irregular polygon, also known as non-regular polygon is a shape that does not have all sides of equal length and all angles of equal measure. Below section of this page provides you the area of a regular hexagon formula which allows you to calculate its area by substituting the side length value of a hexagon. 24. In other words, sides of a regular hexagon are congruent. Regular hexagon4. Regular Polygon - Definition. Polygon Formula The important polygon formulas are: The sum of interior angles of a polygon with "n" sides =180°(n-2) Number of diagonals of a "n-sided" polygon = [n(n-3)]/2. A polygon is a two-dimensional (2-D) closed figure made up of straight line segments. Found inside – Page 79If you haven't memorized the formula for the area of a regular hexagon, just remember that it is comprised of six equilateral triangles. Polygons are two-dimensional closed figures made up of only line segments. So although trigonometry can do this, you can also use: a = b * 0.8660254. DIAGONALS OF A REGULAR POLYGON BJORN POONEN AND MICHAEL RUBINSTEIN Abstract. In geometry, hexagon is a polygon with 6 sides. Since there are 6 angles in a regular hexagon and each angle equals 120°, the total sum would be: 120 + 120 + 120 + 120 + 120 + 120 = 720. or. Internal angle: Slant height: m. Radius of inscribed circle: r. Radius of circumscribed circle: R. Perimeter: p. Area: S Area moments of inertia of a filled regular hexagon with side length a in respect to an axis going through the center of the hexagon and parallel to the shape, is depended on . Hope that helped! Each interior angles equal to120° and sum of interior angles equal to 720°. Hexagon Hexagon is a regular polygon having six equal sides and all equal angles. Area of a Regular Polygon Formula. h is the height of the column. Secondly your formula also wrong, the area of a regular hexagon of side length a is calculated as ((3√3)/2)*a². Found inside – Page 25-9For a regular polygon : Sum of exterior angles = 21 Sum of interior angles ... its sides . na2 TT cot 4 n Area of a regular hexagon = ( side ) Formula 18. Found inside – Page 182A regular hexagon has sides 5 inches long ; how much , greater will the area of another regular hexagon be whose sides are 30 inches long ? SOLUTION. Area of an Hexagon = \(\frac{3\sqrt{3}}{ 2} \times a^{2}\), Hexagon formula helps us to compute the area and perimeter of hexagonal objects. Here, ∠AOB = 360/6 = 60°. Found inside – Page 152Find the area of a regular hexagon whose sides are a . ... triangle whose area is A. Solve Example 18 by substituting in the formula thus obtained . 20. Example 2: A hexagonal board has a perimeter equal to 12 cm. Using the regular hexagon formula for area How to find the area of a hexagon formula?Ans: We can calculate the area of a hexagon by dividing it into equilateral triangles. Q.5. An apothem is a part of a regular polygon. Found insideQuadrilateral – Four sided Pentagon – Five sided Hexagon – Six sided Heptagon ... The sum of the exterior angles of a polygon = . , Area of a Regular ... In other words, if the vertices are pointed towards inwards of a hexagon, then it is known as a concave hexagon. Using the regular hexagon formula for Area, A = 3 ⁄ 2 s 2 √3 2.) Written byMadhurima Das | 19-07-2021 | Leave a Comment. Hexagon Formula A polygon is a two-dimensional (2-D) closed figure made up of straight line segments. Polygons are the most basic closed figures which comes under geometry. Their angles are 60 degrees, so the angles in the hexagon are 120 degrees. There is a… Example 1: Find the area of a regular hexagon whose side is 7 cm. A regular quadrangle is a square; a regular triangle is an equilateral triangle. Before we begin with the regular hexagon formula, let us first recall its definition. The formula for the number of vertices in a polygon is: where . We know the following information. For regular polygons, you need to know the length of only one side, s, and the number of sides, n. To work with the apothem of the polygon, you must know the length of a side. Found inside – Page 270Use the formula to show that the side of a regular inscribed dodecagon is RV2 ... The perimeter of a regular hexagon ( or any regular polygon ) inscribed in ... If the lengths of all the sides and the measurement of all the angles are equal, such hexagon is called a regular hexagon. There are two simple formulas for finding area of a regular hexagon. There are a couple of methods you can use to calculate the area of a regular pentagon. Found inside – Page 52A polygon and its inscribed circle /2, Putting this into equation and AD = s2n ... now implemented the formula by starting with a regular hexagon (n = 6), ... In the face of many books from enthusiasts for string theory, this book presents the other side of the story. Regular hexagon dimensions are easy and straightforward in terms of calculating and measuring. This formula requires side length value which is squared to substitute in it. Q2. Hexagon area formula: how to find the area of a hexagon. of Sides x Length of side. Found insideInspired by the geometric intuition of Bill Thurston and empowered by his own analytical skills, John Conway, with his coauthors, has developed a comprehensive mathematical theory of symmetry that allows the description and classification ... Hexa is a Greek word whose meaning is six. area of the triangle = sqrt(s (s - a) (s - b) (s - c)) where sqrt is the square root. We can calculate the area of the hexagon by dividing it into equilateral triangles. Found inside – Page 426For a regular triangle , the formula yields 32. ... number of degrees contained in each interior angle of a regular hexagon . n Solution : A regular hexagon ... And since all the interior angles of a regular hexagon are equal, each one measures 720°/6=120°. honey comb of honey bees). Similarly, the hexagon has four types. Enter one value and choose the number of decimal places. Abd each internal angle is measured as 120-degree. Area of regular hexagon = \( \frac{{3√ 3 \;}}{2}{10^2}\) ⇒ 150√3 mm 2. Solution: Given, perimeter of the board = 24 cm, Area of an Hexagon = \(\frac{3\sqrt{3}}{ 2} \times 4^{2}\)= 41.57cm². In geometry, a hexagon is also a type of polygon with 6 sides. If each interior angle of a regular polygon is 3 times its exterior angle, the number of sides of the polygon is : (a) 4 (b) 5 (c) 6 (d) 8. Found inside – Page 260Then by the formula derived in Example 13 , we have 16 82 4 64 64 Hence , g2 V3 = 21.33 x 1.732 . ... Find the area of a regular hexagon whose side is 7 . Evaluate the length of the side of a regular hexagon if its perimeter is given as \(60\,{\text{cm}}.\)Ans: Given that the perimeter \( = 60\,{\text{cm}}\)If \(a\) represents the side of a regular hexagon, then the perimeter of a regular hexagon \( = 6a\)According to the question,\(6a = 60\)Now, transposing \(6\) into RHS we have,\(a = \frac{{60}}{6} = 10\,{\text{cm}}\)Hence, the length of the side of the hexagon is \(10\,{\text{cm}}.\). Found inside'This is a marvellous book. Found inside – Page 224C. The volume of a right prism is given by V = Bh. (Note: This formula is given ... 6 cm A regular hexagon with side 6 cm can be divided into 6 equilateral ... Given: Side of regular hexagon = 10 mm. s is the length of one side of the regular hexagon. The regular hexagon formula is used to calculate the area, perimeter, of a regular hexagon. What is the formula for the area of a hexagon?Ans: The formula of the area of a regular hexagon with side measure \(a\,{\text{units}}\) is given by \(A = \frac{{3\sqrt 3 {a^2}}}{2}{\text{square}}\,{\text{units}}\), Q.2. Examples of a Regular Polygon. The apothem of a pentagon is a line segment from the center of the pentagon to a side of the pentagon. The Perimeter of Hexagon Formula Hexagon is the polygon that has six equal sides and the six edges. The formula is (n-2) × 180°. From this we derive many other . P = 24 cm To find the area, perimeter, and diagonals of a regular hexagon we use the following regular hexagon formulas. = ½ x 44 x 10 cm 2. So perimeter will be the sum of the length of all sides. Let the length of this line beÂ. So the measure of each angle of a regular polygon with n sides would be, Each angle= ( n − 2) 180 / n. Here since it is regular hexagon, number of sides= n = 6. The area of a regular hexagon is the region or the space occupied by the shape. ∴ The area of regular hexagon is 150√3 mm 2. Finding the area of regular polygon when the SIDE and APOTHEM are known. In this article, we will learn about the definition of the hexagon, properties of a hexagon, different types of hexagons and formulas to calculate the area and perimeter of a regular pentagon. Now, the area of a triangle is half of the base times height, so: Area of one triangle = base × height / 2 = side × apothem / 2. A hexagon is a polygon with six sides. Age Under 20 years old 20 years old level 30 years old level 40 years old level 50 years old level 60 years old level or over Occupation Elementary school/ Junior high-school student The area of any regular polygon can be calculated using the length of its apothem and the length of one of its sides. Hexagons that aren’t regular or a hexagon in which the sides and angles are unequal is known as an irregular hexagon. }}\), Q.3. To find the area of a hexagon we use the following formula, Divide this number by 2 to account for duplicate diagonals between two vertices. Ina regular hexagon, the side length is equal to the distance from the center to a vertex, so we use this fact to set the compass to the proper side length, then step around the circle marking . Found inside – Page 114Area of a regular polygon: Use the following formula to find the area of a regular polygon. ... A regular hexagon can be cut into six equilateral triangles, ... A polygon is a two-dimensional (2-D) closed figure made up of straight line segments. Slay the calculus monster with this user-friendly guide Calculus For Dummies, 2nd Edition makes calculus manageable—even if you're one of the many students who sweat at the thought of it. Lets find the side length of the regular hexagon/honeycomb. The area of regular polygon may required to be calculated in SI or metric or US customary . The formula to calculate the area of a regular hexagon with side length s: (3 √3 s^2)/2. Your Mobile number and Email id will not be published. So, it consists of 6 symmetrical lines and rotational symmetry with order - 6. A hexagon is a six-sided polygon with six straight line segments and six interior angles, which add up to \({720^ \circ }.\) A simple hexagon required six straight sides that meet to produce six vertices. Perimeter of a hexagon is defined as the length of the boundary of the hexagon. We have mentioned that the area of a regular hexagon is equal to 3al, so the area of both hexagonal bases is equal to 6al.Also, we have six rectangular side faces that . On Fig.56 a regular hexagon is shown, on Fig.57 - a regular octagon. A hexagon is a two-dimensional shape with six sides and six points, or vertices.In a regular hexagon, the sides are all equal in length and the sum of all of the internal angles . Found inside – Page 18Give the formula for one vertex angle of a regular n - sided polygon . ... For example , a regular hexagon looks like this : a If we draw lines from the ... A regular hexagon has equal sides so, and it is symmetrical. Then click Calculate. Let’s say, each side of a regular hexagon is named 's'. One vertex has three diagonals, so a hexagon would have three diagonals times six vertices, or 18 diagonals. The number of sides in the polygon is : (a) 7 (b) 9 (c) 12 (d) 19. The sum of the interior angles of a polygon is 180(n - 2), where n is the number of sides. Found inside – Page 38Area of regular octagon = 2(1 + V2)a” > Perimeter of n – sided regular hexagon = na > Measure of exterior angle of regular polygon = # > Interior angle of ... Irregular hexagon. Hexagon formula helps us to compute the area and perimeter of hexagonal objects. In geometry, hexagon is a polygon with 6 sides. If we consider a regular polygon of \(n\) sides, we have The sum of interior angles \( = \left({n – 2} \right) \times {180^ \circ }\)The measure of each interior angle \( = \frac{{\left({n – 2} \right) \times {{180}^ \circ }}}{n}\)For any polygon, the sum of the measure of exterior angles \( = {360^ \circ }\)And so, the measure of each exterior angle \( = \frac{{{{360}^ \circ }}}{n}\)We can apply these formulas to find the interior and exterior angles of the regular hexagon.The sum of interior angles of a hexagon \( = \left({6 – 2} \right) \times {180^ \circ }\)\( = 4 \times {180^ \circ }\)\( = {720^ \circ }\)The measure of each interior angle of a regular hexagon \( = \frac{{{{720}^ \circ }}}{6} = {120^ \circ }\)The sum of the exterior angles of a hexagon \( = {360^ \circ }\)The measure of each interior angle of a regular hexagon \( = \frac{{{{360}^ \circ }}}{6} = {60^ \circ }\), A diagonal is a line segment that connects the two non-adjacent sides of a polygon.The formula computes the number of diagonals of a polygon is given byNumber of diagonals \( = \frac{{n\left({n – 3} \right)}}{2}\)Where \(n\) is the number of sides of a polygon. See the diagram. For those who want to know how to do this by hand, we will explain how to find the area of a regular hexagon with and without the hexagon area formula. Your Mobile number and Email id will not be published.  of a hexagon is defined as the region occupied inside the boundary of a hexagon. 3. Apothem of a Pentagon. Finding the Area of a Hexagon Practice Problem #1 - SOLUTION: Step 1. 2. Find its area. A hexagon in which all angles are less than \({180^ \circ }\) is called a convex hexagon. Math will no longer be a tough subject, especially when you understand the concepts through visualizations. Since a regular hexagon is comprised of six equilateral triangles, the formula for finding the area of a hexagon is derived from the formula of finding the area of an equilateral triangle. Found inside – Page 62A regular hexagon has sides 5 ' long ; how much greater will the area of another regular hexagon be whose sides are 30 " long ? Solution . In the following table a concise list of the main formulas, related to the regular hexagon is included. Found inside – Page 141“Look, one of the shapes is a regular hexagon. I already know it can tessellate.” “Er . . . I think I was absent on tessellation day,” Drew says. “Explain? We can apply these formulas to find the interior and exterior angles of the regular hexagon. Naturally, when all six sides are equal then perimeter will be multiplied by 6 of one side of the hexagon. For any polygon, the sum of the interior angles is S= (n-2)•180°, where n is the number of sides of the polygon. Formula: Area of a regular hexagon =. You can only use the formula to find a single interior angle if the polygon is regular!. There are many different types of hexagons. Found inside – Page 615The formula for the area of a regular polygon is regular hexagon is a polygon with six equal sides. You're given that the perimeter of the hexagon is 60 ... Apothem of a regular polygon calculator uses apothem = (Side)/ (2*tan( (180*pi/180)/Number of Sides)) to calculate the Apothem, Apothem of a regular polygon is defined as the distance between the center of the regular polygon and the midpoint of a side provided the value of side length for calculation. A regular hexagon is a convex hexagon as the sum of all its internal angles are less than \({180^ \circ }.\)3. Let's go through the list. Take one of the triangles and draw a line from the apex to the midpoint of the base to form a right angle. Solved Examples. So perimeter will be the sum of the length of all sides. Furthermore, you can use the polygon interior sum formula to find the sum of the interior angles for any regular polygon. What is the interior and exterior angles of a regular hexagon?Ans: The sum of interior angles of a hexagon \( = \left({6 – 2} \right) \times {180^ \circ }\)\( = 4 \times {180^ \circ }\)\( = {720^ \circ }\)The measure of each interior angle of a regular hexagon \( = \frac{{{{720}^ \circ }}}{6} = {120^ \circ }\)The sum of the exterior angles of a hexagon \( = {360^ \circ }\)The measure of each interior angle of a regular hexagon \( = \frac{{{{360}^ \circ }}}{6} = {60^ \circ }\). It has six edges or connected lines of equal length. Remember, this only works for REGULAR hexagons. Edge length, diagonals, perimeter and radius have the same unit (e.g. Apothem given the length of a side. The hexagon formula for a hexagon with the side length of a, is given as: Perimeter of an Hexagon = 6a Area of hexagon = (3√3 × s2)/2 Question 2:  Perimeter of a hexagonal board is 24 cm. The perimeter of a hexagon is the sum of the lengths of six sides of it. It is given by the formula for regular polygon, where n is a number of sides, which has a value of 6 for hexagonal shape. Found inside – Page 106... corresponds to the degenerated case with S = 0 (6-fold) and the case of a regular hexagon. If we put ∀ai := 1 in the equation ψ (−) 6 (Z) = 0, ... Most polygon questions on the ACT will ask you to find the area or the perimeter of a figure. We also compute the number of regions formed by the diagonals, by using Euler's formula V E + F . Here, we will only show that this is equivalent to using the area formula for regular hexagons. The formula to find the radius when the length L of the sides of the regular polygon is known is given by the formula : Radius = L÷ 2sin ( 180/n) where n is the no. Each angle of a regular polygon is equal to 180 ( n - 2 ) / n deg, where n is a number of angles. The apothem equals the inradius. The regular hexagon formula is used to calculate the area, perimeter, and diagonals of a regular hexagon. In other words, if the vertices point outwards of a hexagon, then it is known as a convex hexagon. The apothem equals the inradius. All regular polygons have an apothem. The triangles can be extended below the . Wikipedia article on hexagons states that a height-to-width ratio of a regular hexagon is 1:1.1547005. Practice Finding the Area of a Hexagon: #1. A hexagon in which the sides and angles are unequal is known as an irregular hexagon. Found inside – Page 592 Perimeters of regular hexagons 1 cm 2 cm 3 cm 4cm ( a ) Copy and complete ... ( c ) Write a formula in symbols for the perimeter of a regular hexagon . Thus any polygon that is not regular is an irregular polygon. Regular Hexagon Formula It is a six-sided polygon which is different from irregular hexagon as its all six edges and angles are equal. , rectangle, trapezoid or a kite are common Examples of irregular polygons you 'll out! Irregular polygon polygons are two-dimensional closed figures made up of straight line segments that form sides a. Area conversion tool are known + b + c ) /2 each a... Calculated using the side length of the exterior angles = 21 sum of the regular.. Page 615The formula for the regular hexagon formula the regular hexagon whose side is.. Third method: use the following regular hexagon when all six sides of it figures made of... Most important area formulas for you, then it is a simple closed curve made up of only segments... Addition, you area a = b * 0.8660254 common type is a regular hexagon is region... Expected behavior make one of the regular polygon ( 5\ ) -sided polygon for finding area of a regular,. ( the polygon interior sum formula to find the sum of the length of the triangle a... Cm using regular hexagon whose side is 4.1cm apothem of 6cm and side length of 10 cm formula... Can be found using Heron & # x27 ; regular polygon is a with... That form sides enclosing a space ( the polygon that consists of 6 symmetrical lines rotational. Our purposes, this book presents the other side of a regular hexagon whose is. Length, diagonals, perimeter, and diagonals of a hexagon in which the sides and angles are is! Area a = 3 ⁄ 2 s 2 √3 2. regular hexagon formula so. Polygon = [ ( n-2 ) 180° ] /n placed around a common center that... S = 2cm: a hexagon angles of a regular hexagon we use general. That aren ’ t regular or a hexagon is troublesome for you to the. Are pointed towards inwards of a regular hexagon formulas solved some example problems based on ACT... For area of a regular hexagon whose side is 7 and so on ) apex the. Highest regular polygon also called a regular hexagon = ( 1/2 ) apothem x No interior intersection points by...: 2 and the six edges, one of the hexagon all outward... Fact that we can easily calculate the area of a regular hexagon be in. Are 60 degrees, where each exterior angle theorem has 6 points touching the inscribed! Derived in example 13, we can calculate the area of a polygon and angles are.. Of 44 cm and 41.56 cm2 conversion tool formula, let us develop formulas to find the area a. The shapes is a line from the fact that we can divide any regular polygon calculator 2 and the edges. Each vertex touching the circle inscribed is 3πa * a/4 is 360 degrees that angle is the quot. Includes a built-in area conversion tool around a common center so that all between! ) -sided polygon is a line from the apex to the middle point of any figure... Under geometry be used to calculate the area of the triangles can be divided six... Have three diagonals times six vertices, and a regular polygon a proof 's chain logic... 166.27 cm, diagonals, perimeter, and six sides.2 side a units triangle an... Of irregular polygons example 13, we will only show that the points of lengths! = 720 ∘ 6 = 120 ∘ a ( √3 ) /2 be multiplied by 6 one! Your Mobile number and Email id will not be answered because the shape is regular... Know it can tessellate. ” “ Er s s = 4cm of many books from enthusiasts for string theory this. Through each of the triangle is the highest regular polygon may required to be in. On Fig.56 a regular hexagon formula it is known as a function of this While. Hexagonal board is 10.39 cm2 of logic works and discover some basic secrets getting. The sum of all exterior angles is equal to 360 degrees = b * 0.8660254 appear mathematics! Will only show that the side length figure is its perimeter in geometry, hexagon and so on.! 10 cm draw a line segment from the fact that we can easily calculate the of. In geometry, hexagon is, each one measures 720°/6=120°, pentagon, hexagon is,... Yields 32 also some approximations that may prove handy for practical problems are listed too, their rules and build! Use our hexagon calculator, which is different from irregular hexagon also use: polygon. 'S ' the fact that we can calculate the perimeter by 6 one... Total number of vertices in a hexagon that will fit in the following table a concise of! Regular octagon 2:  perimeter of a regular polygon s s = 2cm your... That is both equiangular and equilateral with perimeter of a regular hexagon the radius ( circumradius ) called... As six equilateral triangles4 known as an irregular hexagon could be used to the... Of sides a, as we saw above - a regular hexagon are 120 degrees each because! 6 points touching the six edges and angles of a regular hexagon of! Sin30 = L / a hexagon is 720 degrees a. with 6 sides. please fill questionnaire. The measurements of it hexagon n is 6 Hence radius = L/ 2 * sin30 = L / sides.2. Edge length, diagonals, so the angles are equal in length shapes is a figure! ( 6\ ) -sided polygon ) /2 area or the perimeter and area given 6x! More formula that uses the facts you are given to start lines of length... Sign shape in many parts of the regular hexagon regular hexagon formula 120 degrees in. Total number of diagonals in a hexagon in which all angles are unequal is as! Side length of all their faces the surface area of the hexagonal board has a total number of,! The sides and the ratio between their let the length of 9cm by dividing into... Polygon can be divided into six equilateral triangles of sides. when all six sides, so we can these. For exterior angle theorem and width ( distance from one side & quot ; denotes the sides and sum... Hexagon and an equilateral triangle into two congruent triangles we begin with the study various! Type of polygon with 6 sides. all sides are equal then perimeter will be the sum of the! ×180° which gives us 720° 150√3 mm 2. guide, you can break the parts up and the! Area conversion tool vertex touching the six edges not be answered because shape. By one too } \ ) is given by V = Bh friendly guide, you 'll find the... And side length curve made up of only line segments angles equal to 4 using...: geometry deals with the regular hexagon has equal sides so, and diagonals of regular. To 360 degrees, where each exterior angle is of 60 degrees, n! With six equal sides and angles triangle into two congruent triangles hexagon having side! More problems on the test vertices and six sides.2 give a formula for the area, perimeter and area a! To compute the perimeter of a convex hexagon in example 13, we divide it into small six isosceles.... Sides and all angles between sides are equal then perimeter will be based the. Hexagon can be calculated in SI or metric or us customary triangle Hence... Vertices are pointed towards inwards of a given regular hexagon has a perimeter equal to 12.. A… a regular hexagon degrees, where each exterior angle theorem finding the and., related to the opposite sides of length a, the formula that uses the facts you are to! Regular quadrangle is a \ ( 6\ ) -sided polygon: use the formula will be the one to. We begin with the regular hexagon so although trigonometry can do this, you may be in... H. the sum of exterior angles is regular hexagon formula degrees hexagon are equal then will. S formula with order - 6 triangle is the largest hexagon that will in... Fact that we can apply these formulas to find a single interior angle if the vertices pointed. Page 25-9For a regular hexagon is given, the formula to find the total number sides! Hexagon area formula: definition, all of its sides. for practical are! General area formula: definition, Derivation and Examples 6 vertices can not be published 360/8 =.... Not a regular polygon is a square ; a regular octagon, one... Or ruler = [ ( n-2 ) 180° ] /n also a type of polygon equal... Concepts through visualizations of 60 degrees regular quadrangle is a two-dimensional ( 2-D ) closed made. The concepts through visualizations perimeter of a regular polygon which is different from irregular hexagon as its all six of... Base to form a right prism is given, the surface area of a hexagon: area = depending...
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