Question

A pentagon can be divided into five congruent triangles as shown. The function y = 5 tan θ models the height of each triangle. What is the area of the pentagon if θ = 54°? Round to the nearest square foot.pentagon(1 point)Responses9 ft29 ft 286 ft286 ft 2172 ft2172 ft 2344 ft2

Answer 1

[AI-generated answer — Bot GPT 3.5]

The height of each triangle is given by y = 5 tan θ, where θ = 54°.

Plugging in θ = 54°, we get:
y = 5 tan 54°
y = 5 * 1.3764
y ≈ 6.882 ft

The area of each triangle is given by A = 1/2 * base * height.
Since the base of each triangle is 5 ft (due to it being a side of the pentagon), the area of each triangle is:
A = 1/2 * 5 ft * 6.882 ft
A ≈ 17.205 ft²

Since there are five congruent triangles in the pentagon, the total area of the pentagon is:
Total Area = 5 * 17.205 ft²
Total Area ≈ 86.025 ft²

Therefore, the area of the pentagon is approximately 86 ft².