subject: Area Formula Pentagon [print this page] 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.
