![]() The easiest way is to use our hexagon calculator, which includes a built-in area conversion tool. Seven 51.We will now take a look at how to find the area of a hexagon using different tricks. Heptagon symmetryĪ regular heptagon has 7 lines of symmetry and a rotational symmetry of order 7, meaning that it can be rotated in such a way that it will look the same as the original shape 7 times in 360°. Since the sum of the interior angles of a triangle is 180°, the sum of the interior angles of the heptagon is 5 × 180° = 900°. The sum of interior angles of the five triangles equals the sum of interior angles of the heptagon. The blue lines above show just one way to divide the heptagon into triangles there are others. The sum of the interior angles of a heptagon equals 900°.Īs shown in the figure above, four diagonals can be drawn to divide the heptagon into five triangles. There are 4 diagonals extending from each of the 7 vertices of the heptagon above creating a total of 14 diagonals. A total of fourteen distinct diagonals can be drawn for a heptagon. For a regular heptagon, each of the seven interior angles measures ~128.57°.Įach of the exterior angles measures ~51.43°.Ī diagonal is a line segment joining two non-consecutive vertices. For irregular heptagons, the individual interior and exterior angle measures will vary. The sum of the interior angles of a heptagon is 900° and the sum of the exterior angles is 360°. The formula to find the sum of the interior angles of any polygon is Where n is the number of sides in the polygon. The formula to find the measure of the interior angles of any regular polygon is The perimeter formula for an irregular heptagon is simply the sum of each of its sides. The regular heptagon perimeter formula is This formula simplifies to approximately: The formula for the area of a regular heptagon is: The following are properties of all heptagons:īelow are formulas for finding the area, perimeter, measure of the interior angles, and sum of the interior angles of a heptagon. Notice that two of the interior angles measure greater than 180°, so the heptagon is concave. The figure below shows a concave heptagon example: Because at least 1 angle of the heptagon must me greater than 180°, but not all can equal 180° (since the interior angles of a heptagon always sum to 900°), all concave heptagons are irregular. For any interior angle that measures greater than 180°, there is also a corresponding diagonal that will lie outside of the boundaries of the heptagon. Concave heptagonĪ concave heptagon is a heptagon in which at least one interior angle measures greater than 180°. Notice that none of the interior angles measure greater than 180°, but at the same time, the sides and interior angles are not all congruent. The figure below shows an irregular convex heptagon example. ![]() A regular heptagon is always a convex heptagon, but a convex heptagon can either be regular or irregular. As a result, all of the diagonals of a convex hexagon lie within the boundaries of the shape. Convex heptagonĪ convex heptagon is a heptagon in which all interior angles measure less than 180°. An irregular heptagon can be either concave or convex. The figure below shows an irregular heptagon example:Īs can be seen in the figure, not all of the sides and angles of the heptagon are congruent, so it is irregular. 7 exterior angles measuring 51.43° each.Īn irregular heptagon is a heptagon that has varying measures of sides and interior angles.7 interior angles measuring ~128.57° each.The figure below shows a regular heptagon example:Ī regular heptagon has the following properties: Regular heptagonĪ regular heptagon is a heptagon whose sides and interior angles are all equal in measure. Heptagons are classified as regular or irregular and concave or convex. The figure below shows a few examples of the shapes that a heptagon can take on. Two real-life heptagon examples include the fifty pence and twenty pence coins in the UK. What is a heptagonĪ heptagon is defined as a 7-sided, closed, two-dimensional shape. A heptagon is also sometimes called a septagon. Home / geometry / shape / heptagon HeptagonĪ heptagon is a polygon that has seven sides (Hepta- means seven) and seven interior angles.
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