Heptagon

In Geometry, the shape that is bounded by at least three straight lines or at least three interior angles is called polygons. The most common examples of polygons are

  • Triangle ( 3 sided polygon)
  • Quadrilateral ( 4 sided polygon)
  • Pentagon ( 5 sided polygon)
  • Hexagon ( 6 sided polygon)
  • Heptagon ( 7 sided polygon)
  • Octagon ( 8 sided polygon) and so on.

Types of polygons

In this article, let’s discuss the seven-sided polygon called “Heptagon” with proper definition, shape, sides, properties along with its formula in detail.

Heptagon Definition

Heptagon

A 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 shape

As in other polygons like a triangle, quadrilateral, pentagon, hexagon, the heptagon is also a polygon that contains seven sides and seven angles.

Depending on the angles and diagonals, there are different types of a heptagon, such as

  • Regular and Irregular Heptagon
  • Convex and Concave Heptagon

Regular and Irregular Heptagon

If 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.

Regular and Irregular Heptagon

Convex and Concave Heptagon

If 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.

Convex and Concave Heptagon

 

Heptagon Properties

Some properties of heptagons are as follows:

  • In heptagon, the sum of the interior angles is equal to 900 degrees
  • The sum of exterior angles of a heptagon is 360 degrees
  • For regular heptagon, the measure of the interior angle is about 128.57 degrees
  • The measure of the central angle of a regular heptagon is approximately 51.43 degrees
  • The number of diagonals in a heptagon is 14
  • Regular heptagons are also known as convex heptagons
  • The number of triangles formed in a heptagon is 5

Area of a Heptagon

For a regular heptagon with side length “a”, then the formula to find the area of a heptagon is given as

Area of a heptagon, \(A = \frac{7}{4}a^{2}\cot \frac{\pi }{7}\) Square units

The above equation is approximately equal to

Area of a Heptagon, A = 3.634a2 square units

Perimeter of Heptagon

Since 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 problem

Question:

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 91.075 cm2

The perimeter of a heptagon, P = 7a units

P = 7(5)

P = 35 cm

Hence, the perimeter of a heptagon is 35 cm.

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