Heptagon: Shape, Diagonals, Types, Properties, Angle sum property, perimeter and Area of heptagon

In geometry, a shape formed by joining straight lines is called a polygon. A polygon can have any number of sides, the smallest being a triangle which is a three-sided polygon. Polygons are geometric shapes named on the basis of a number of sides. For example,

Triangle- a three-sided polygon
Quadrilateral- a four-sided polygon. Examples: square, rectangle, parallelogram
Pentagon- a five-sided polygon
Hexagon- a six-sided polygon
Heptagon- a seven-sided polygon

and so on depending on the number of sides and interior angles.

Note: A circle is known as a polygon that has an infinite number of sides.

Heptagon

A heptagon is a closed polygon consisting of seven interior angles. It comprises of seven sides and is also known as a septagon. For example,

The above polygon is a heptagon with sides AB, BC, CD, DE, EF, FG and GA.

Diagonals of a heptagon

A heptagon has 14 diagonals as AD, AE, BE, BF, CF, CG, DA, DE, EA, EB, FB, FC, GC and GD in the figure given below.

Types of heptagon

Regular heptagon - The heptagon which has all its sides and angles equal to each other is called a regular heptagon.
Irregular heptagon - If the heptagon has sides and interior angles different from each other it is called an irregular heptagon.
Convex heptagon - A heptagon having all the diagonals inwards is called a convex diagonal.
Concave heptagon - A heptagon having all its diagonals outwards and one of its interior angles greater than 180°.

Properties of heptagon

Some of the common properties of heptagon are as below:

A regular heptagon is a convex polygon.
A heptagon has 7 sides.
It has 7 interior angles.
For a regular heptagon, the adjacent sides meet each other at an angle of 128.57°.
It has 14 diagonals.
The sum of all its interior angles is 900°.

Angle sum property of a heptagon

The angle sum property of a heptagon is 900 i.e. the sum of all the interior angles of a heptagon is 900°. It can be calculated by the formula

(n – 2). 180°

where n is the number of sides.

Interior angles of a heptagon

For a regular polygon, the measure of each interior angle can be calculated by

[(n – 2) . 180°]/n.

The perimeter of a heptagon

The perimeter of a heptagon is the measure of the total boundary length of the heptagon. It is calculated by adding all the sides of the given heptagon. For a regular heptagon, the perimeter of the heptagon is obtained as the product of measure of one of its sides by 7.

Perimeter of a regular heptagon = 7 . length of a side