Created By : Abhinandan Kumar

Reviewed By : Rajashekhar Valipishetty

Last Updated : May 29, 2023

The perimeter of a pentagon is the entire distance covered by the pentagon. If you talk about pentagon perimeter only, then it's basically the total length of the pentagon. In a simple way, you can say that perimeter is the summation of 5 sides of the pentagon.

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Pentagon Side

Formula to Calculate Pentagon Perimeter

Perimeter of a pentagon can be calculated by using any one of the formula mentioned here

If you know the length of side of a pentagon, then

Pentagon Perimeter = 5 * s, where s is the length of side of a pentagon.

If you know the diagonal length, then

Perimeter of a pentagon = (10 * d) / (1 + √5), where d is the length of diagonal of a pentagon.

If you know the pentagon area, then

Perimeter of a pentagon = 5 * √[(4 * a) / (√(5 (5 + 2 √5))]

Step by Step Process to find Pentagon Perimeter

To calculate the perimeter of a pentagon, you just have to follow some easy steps mentioned here:

• Once go through the given information, and find out the length of side of a pentagon and make a not of that value.
• Multiply that value with 5.
• Answer is the pentagon perimeter

Examples of Pentagon Perimeter

Example 1: One side of a regular pentagon is 10 cm. Find the perimeter of the pentagon?

Solution:

Given that,

The length of side of pentagon s = 10 cm

Pentagon perimeter = 5 * s

= 5 * 10

= 50

∴ Perimeter of a pentagon is 50 cm.

Example 2: The apothem of a regular pentagon is 3 cm. What is the perimeter of this pentagon?

Solution:

In order to get the length of one side of a pentagon, draw a right triangle from the apothem and the top angle.

Angle measured is 360 / 5 = 72°

where the sum of all the angles around the center of the pentagon sum up to 360° and the 5 is for the number of sides. We can do this because all of the interior angles of the pentagon will be equal because it is regular. Then, this answer needs to be divided by 2 because the pictured right triangle is half of a larger isosceles triangle.

72° / 2 = 36°

Marked angle is 36°.

Tan (θ) = Opposite side / adjacent side

tan 36° = x / 3

0.727 = x / 3

x = 2.181

So, side of a pentagon = 2.181

Perimeter of pentagon = 5 * side

= 5 * 2.181

= 10.905

∴ Perimeter of a pentagon is 10.905 cm.

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Frequently Asked Questions on Pentagon Perimeter

1. What is meant by perimeter of a pentagon?

Perimeter is the length of outline of the perimeter. That means sum of length of all sides of a pentagon. For a regular pentagon, perimeter is 5 * side length.

2. How do you find the perimeter of a 5 sided polygon using calculator?

Enter the length of side of a pentagon in the input section and press on the calculate button which is located under the input box to get the accurate output i.e perimeter of a pentagon in seconds.

3. Is the perimeter of a Pentagon five times the length of one side?

Yes, perimeter of a regular pentagon is 5 times the length of one side of pentagon. Here is the proof for that. Perimeter is defined as the sum of all sides of a polygon.

Let us say, side of pentagon is a.

Perimeter according to the formula is 5 * a.

According to the definition perimeter is a + a + a + a + a = 5 * a.

4. Find the perimeter of a pentagon having area 43 cm2?

Area = 43 cm2

Perimeter = 5 * √[(4 * a) / (√(5 (5 + 2 √5))]

= 5 * √[(4 * 43) / (√(5 (5 + 2 √5))]

= 5 * √[(172) / (√(5 * (9.472))]

= 5 * √[(172) / (6.88)]

= 5 * 5 = 25