A pentegon can be divided into five congruent triangles as shown. the function y=5 tan theta models the height of each triangle. what is the area of the pentagon if theta=54 degrees?

We are required to calculate the area of the pentagon whose height is given by y=5 tan theta

where; theta=54°

but

tan theta=[opposite]/[adjacent]

thus

opposite=adjacent tan theta

since

5tan54=opposite

adjacent=5

Therefore the base of the pentagon will be

(5+5) = 10

Area of a triangle is given by:

A=1/2 (base*height) sin theta

The area of one triangle forming the pentagon will be:

A=1/2 * (10*5tan54) * sin54

A=27.84 square units

Thus the area of pentagon will be:

Area = (# triangles) * (area of one triangle)

=27.84*5

=139.2 square units