Question

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.

Answer 1

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