Area Formula Pentagon

Introduction to area formula pentagon:

Introduction to area formula pentagon:

Pentagon has five sides in its structure. It is one of the type of polygons. Side length of the pentagon is always equal. The interior angle of the pentagon is 540. Each interior angle value of the pentagon is 108. All the pentagons are divided by three triangles. The pentagon has the rotation and reflection symmetry. They are depends on side length of the pentagon.

Pentagon

Area formula for pentagon:

Area of the pentagon = s2 * 1.72

(or)

Area of the pentagon = (5 / 4)s2 (tan54)

Here, s = side length.

Example Problem for Area Formula Pentagon

Example 1:

Find the area of the pentagon with the side length is 22 cm.

Solution:

Given side length s = 22 cm

Formula:

Area of the pentagon = s2 * 1.72

Substitute the given side length value in the above equation, we get

Area = 222 * 1.72 cm2

= 832.48 cm2

Answer:

Area of the pentagon is 832.48 cm2

Example 2:

Find the area of the pentagon with the side length is 14 cm.

Solution:

Given side length s = 14 cm

Formula:

Area of the pentagon = s2 * 1.72

Substitute the given side length value in the above equation, we get

Area = 142 * 1.72 cm2

= 337.12 cm2

Answer:

Area of the pentagon is 337.12 cm2

Example 3:

Find the area of the pentagon with side length is 8 cm.

Solution:

Given side length is s = 8 cm

Formula:

Area of the pentagon = (5 / 4)s2 (tan54)

Substitute the given side length value in the above equation, we get

Area = (5 / 4) * 82 * (tan54)

= 110.11 cm2

Answer:

The area of the pentagon is 110.11 cm2

Example 4:

Find the side length of the pentagon with the area of the pentagon is 342 cm2

Solution:

Given area is 342 cm2

Formula:

Area of the pentagon = 1.72 * s2

Therefore, side length s = v (Area of the pentagon / 1.72)

Substitute the given value in the above equation, we get

side length s = v (342 / 1.72)

s = 14.10 cm

Answer:

The side length of the pentagon is 14.10 cm.

Practice Problems for Area Formula of Pentagon

Example 1:

Find the area of the pentagon with the side length is 6 cm.

Answer:

The area of the pentagon is 61.92 cm2

Example 2:

Find the side length of the pentagon. Given area is 240 cm2

Answer:

The side length of the pentagon is 11.81 cm.

Example 3:

Find the area of the pentagon with the side length is 42 cm.

Answer:

The area of the pentagon is 3034.08 cm2

by: jeri

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