A pentagon can be divided into 5 congruent triangles. The function y = 5 tanθ models the height of each triangle. What is the area of the pentagon if θ = 54 degrees?

Solution:

The information stated in the problem statement is summarized in the diagram below:

The height of the triangle y = 5tanθ

Tanθ = y/5

The above relationship implies:

y = perpendicular

Base = AD = 5
y = 5tan 54°

   = 5(1.378) 

   = 6.890

Area of the triangle OAB = (1/2)(Base)(Height)

Base AB = 2AD = 2 × 5 = 10

Area of the Triangle OAB = (1/2)(10)(6.890)

=  34.85

Since there are five triangles in a regular pentagon, the area of the pentagon is :

= 5 × 34.85 = 172.25

A pentagon can be divided into 5 congruent triangles. The function y = 5 tanθ models the height of each triangle. What is the area of the pentagon if θ = 54 degrees?

Summary:

The area of the pentagon if θ = 54 degrees is 172.25.