Perimeter of Pentagon

The perimeter of a pentagon is the total distance covered around its edge. The perimeter is always linear. So its units are also linear, such as cm, in, m, ft, or yd.

Formula

The basic formula to find the perimeter of a regular pentagon is given below:

Solved Examples

Find the perimeter of a pentagon whose side length is 7 cm.

Solution:

As we know,
Perimeter (P) = 5s, here s = 7 cm
= 5 Ã— 7
= 35 cm

Finding the perimeter of a pentagon when the RADIUS is known

What is the perimeter of the given pentagon.

Solution:

Here, we will use a formula to find the side length involving the radius to calculate the perimeter.
Side length (s) = 2r Ã— sin(180Â°/n), here n = number of sides of a polygon, i.e. 5
2r Ã— sin(36Â°), here r = 11 cm
= 2 Ã— 11 Ã— sin(36Â°)
= 12.93 cm
Now, as we know,
Perimeter (P) = 5s, here s = 12.93 cm
= 5 Ã— 12.93
= 64.65 cm

Finding the perimeter of a pentagon when the APOTHEM is known

Find the perimeter of a pentagon with an apothem of 8 in.

Solution:

Here, we will use a formula to find the side length involving the apothem to calculate the perimeter.
Side length (s) = 2a Ã— tan(36Â°), here a = 8 in
= 2 Ã— 8 Ã— tan(36Â°)
= 11.62 in
Now, as we know,
Perimeter (P) = 5s, here s = 11.62 in
= 5 Ã— 11.62
= 58.1 in

Finding the perimeter of an irregular pentagon when the SIDES are known

What is the perimeter of the given pentagon.

Solution:

As we know,
Perimeter (P) = sum of all sides, here the sides are 8 cm, 9 cm, 14 cm, 7 cm, and Â 11 cm
= 8 + 9 + 14 + 7 + 11
= 49 cm