A heptagon is a polygon that has seven sides. It is a closed figure having 7 vertices. A heptagon is also sometimes called Septagon. In Geometry, the shape that is bounded by at least three straight lines or at least three interior angles is called polygon. The most common examples of polygons are In this article, let’s discuss the seven-sided polygon called “Heptagon” with proper definition, shape, sides, properties along with its formula in detail. Also, read: Quadrilaterals Heptagon DefinitionA heptagon is a polygon with 7 sides and 7 angles. Sometimes the heptagon is also known as “septagon”. All the sides of a heptagon meet with each other end to end to form a shape. Therefore, The number of heptagon sides = 7 Heptagon shapeDepending on the angles and diagonals, there are different types of heptagon, such as
Regular and Irregular HeptagonIf a heptagon is regular, then all the angles and sides are equal, and the hexagon sides meet each other at an angle of 5π/7 radians or [128(4/7)degrees]. If the heptagon does not have equal side and angle measure, then it is known as irregular heptagon. Convex and Concave HeptagonIf all the diagonals lie inside the heptagon, it is known as convex heptagon. If some of the diagonals lie outside of the heptagon and one or more interior angles are greater than 180 degrees, then the heptagon is known as concave heptagon. Heptagon PropertiesSome properties of heptagons are as follows:
Area of a HeptagonFor a regular heptagon with side length “a”, then the formula to find the area of a heptagon is given as \(\begin{array}{l}\text {Area of a heptagon, }A = \frac{7}{4}a^{2}\cot \frac{\pi }{7} \ \text{Square units}\end{array} \) The above equation is approximately equal to: Area of a Heptagon, A = 3.634a2 square units Perimeter of HeptagonSince all the sides “a” of a regular heptagon are of equal measure, then the perimeter or circumference of a heptagon is written as, The perimeter of a heptagon, P = 7a units Heptagon Solved problemQuestion: Find the area and perimeter of a regular heptagon whose side is 5 cm? Solution: Given: The side of a heptagon, a = 5 cm We know that The area of a heptagon, A = 3.634a2 square units Substitute a = 5 cm in formula, A = 3.634 (5)2 A = 3.634 (25) A = 90.85 cm2 Therefore, the area of a heptagon is 90.85 cm2 The perimeter of a heptagon, P = 7a units P = 7(5) P = 35 cm Hence, the perimeter of a heptagon is 35 cm. Stay tuned with BYJU’S – The Learning App to learn all the interesting Maths concepts and also explore videos to learn with ease.
In maths (geometry), a heptagon is a polygon with seven sides and seven angles. A heptagon has seven straight sides and seven corners i.e. vertices. It is sometimes referred to as a “septagon”.
Regular Heptagons: In a regular heptagon, all the angles and sides are equal. Irregular Heptagon: In an irregular heptagon, the measure of sides and angles are not equal.
Convex Heptagon: In a convex heptagon all its diagonals lies inside it. Concave Heptagon: In a concave heptagon, one or more interior angles are greater than 180 degrees and some diagonals lie outside the polygon.
The angle of a regular heptagon is 5π/7 radians or 128.57 degrees. In a heptagon, the sum of all seven angles is 900 degrees.
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What is the measure of each interior angle of a regular heptagon? Round to the nearest tenth. |