A pentagon can be divided into five congruent triangles. The function t=5 tan theta models the height of each triangle. What is the area of the pentagon if theta=54 degrees? Round to the nearest foot.

We assume that the dimension 5 has units of feet.

The area of each triangle will be

A = (1/2) bh

where b=2 * (5 ft), h = (5 ft) tan (54°)

Then

A = (1/2) (2*5 ft) (5 ft) (tan (54°)

A = 25*tan (54°) ft²

There are 5 such triangles making up this pentagon, so the total area is

total area = 5*25*tan (54°) ft² ≈ 172 ft²