A heptagon is a polygon that has seven sides. That is a closed figure having 7 vertices. A disappearance is also sometimes dubbed Septagon.

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In Geometry, the shape that is bounded by at the very least three straight lines or at the very least three inner angles is referred to as polygon. The most common examples of polygons are

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

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In this article, let’s comment on the seven-sided polygon referred to as “Heptagon” with ideal definition, shape, sides, properties in addition to its formula in detail.

Also, read: Quadrilaterals

Heptagon Definition

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A heptagon is a polygon with 7 sides and 7 angles. Occasionally the heptagon is additionally known as “septagon”. All the political parties of a heptagon accomplish with every other end to finish to type a shape. Therefore,

The variety of heptagon sides = 7

Heptagon shape

Depending top top the angles and diagonals, there room different types of heptagon, such as

Regular and Irregular HeptagonConvex and Concave Heptagon

Regular and also Irregular Heptagon

If a disappear is regular, then every the angles and sides space equal, and the hexagon sides accomplish each various other at an angle of 5π/7 radians or <128(4/7)degrees>. If the heptagon go not have equal side and also angle measure, climate it is recognized as irregular heptagon.

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Convex and Concave Heptagon

If every the diagonals lie within the heptagon, the is recognized as convex heptagon. If some of the diagonals lie outside of the heptagon and also one or much more interior angle are greater than 180 degrees, then the disappear is well-known as concave heptagon.

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Heptagon Properties

Some properties of heptagons are as follows:

In heptagon, the amount of the interior angles is same to 900 degreesThe sum of exterior angle of a disappear is 360 degreesFor continual heptagon, the measure of the inner angle is about 128.57 degreesThe measure up of the central angle of a regular heptagon is around 51.43 degreesThe number of diagonals in a disappear is 14Regular heptagons are additionally known as convex heptagonsThe number of triangles created in a disappear is 5

Area of a Heptagon

For a continual heptagon v side length “a”, climate the formula to uncover the area that a heptagon is offered as

Area that a heptagon, \(A = \frac74a^2\cot \frac\pi 7\) Square units

The over equation is about equal to

Area the a Heptagon, A = 3.634a2 square units

Perimeter the Heptagon

Since every the political parties “a” the a continuous heptagon space of equal measure, climate the perimeter or one of a disappearance is created as,

The perimeter of a heptagon, ns = 7a units

Heptagon solved problem

Question:

Find the area and also perimeter of a continuous heptagon whose next is 5 cm?

Solution:

Given:

The next of a heptagon, a = 5 cm

We know that

The area that a heptagon, A = 3.634a2 square units

Substitute a = 5 centimeter in formula,

A = 3.634 (5)2

A = 3.634 (25)

A = 90.85 cm2

Therefore, the area the a disappear is 90.85 cm2

The perimeter of a heptagon, p = 7a units

P = 7(5)

P = 35 cm

Hence, the perimeter that a heptagon is 35 cm.

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