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. (1 point) Responses 9 ft2 9 ft 2 86 ft2 86 ft 2 172 ft2 172 ft 2 344 ft2
To find the area of the pentagon, we need to find the area of one of the congruent triangles and then multiply by 5.
Given that the function for the height of each triangle is y = 5 tan θ, where θ = 54°, we can plug in the value for θ:
y = 5 tan(54°)
y = 5 * 1.37638 (approximately)
y = 6.8819 feet
Next, we calculate the area of one triangle:
Area = (1/2) * base * height
Area = (1/2) * 5 * 6.8819
Area ≈ 17.2048 square feet
Since there are 5 congruent triangles making up the pentagon, we multiply the area of one triangle by 5:
Total area = 17.2048 * 5
Total area ≈ 86.024 square feet
Rounded to the nearest square foot, the area of the pentagon is 86 ft^2.
Therefore, the correct answer is:
86 ft2