What is the approximate area of a triangular roof with sides 10 ft, 20 ft, and 20 ft?

What is the approximate area of a triangular roof with sides 10 ft, 20 ft, and 20 ft?

• A. 97 sq ft
• B. 89 sq ft
• C. 110 sq ft
• D. 120 sq ft

Answer: (A)

For a triangular roof with sides 20 ft, 20 ft, and base 10 ft, drop a height to the base. This splits the base into two equal segments of 5 ft. The height h satisfies the right triangle relationship: h^2 + 5^2 = 20^2, so h^2 = 400 - 25 = 375, and h ≈ 19.3649 ft. Area = (1/2) × base × height = (1/2) × 10 × 19.3649 ≈ 96.8 square feet, which rounds to about 97 sq ft. This matches the area computed by Heron’s formula as well.

For a triangular roof with sides 20 ft, 20 ft, and base 10 ft, drop a height to the base. This splits the base into two equal segments of 5 ft. The height h satisfies the right triangle relationship: h^2 + 5^2 = 20^2, so h^2 = 400 - 25 = 375, and h ≈ 19.3649 ft.

Area = (1/2) × base × height = (1/2) × 10 × 19.3649 ≈ 96.8 square feet, which rounds to about 97 sq ft. This matches the area computed by Heron’s formula as well.