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

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

• A. 97 sq ft
• B. 90 sq ft
• C. 100 sq ft
• D. 110 sq ft

Answer: (A)

Finding the area uses the triangle formula: area equals base times height divided by two. Here the triangle forms a triangle roof section with a base of 10 feet and two equal sides of 20 feet. The height comes from dropping a line from the top vertex to the midpoint of the base, which creates a right triangle with half the base as 5 feet and a leg of 20 feet. Height = sqrt(20^2 − 5^2) = sqrt(400 − 25) = sqrt(375) ≈ 19.36 feet. Now the area is (1/2) × base × height = (1/2) × 10 × 19.36 ≈ 96.8 square feet. This rounds to about 97 square feet, matching the closest option. In practice, this is the typical way to estimate roof sections when you know the side lengths of the triangular end.

Finding the area uses the triangle formula: area equals base times height divided by two. Here the triangle forms a triangle roof section with a base of 10 feet and two equal sides of 20 feet. The height comes from dropping a line from the top vertex to the midpoint of the base, which creates a right triangle with half the base as 5 feet and a leg of 20 feet. Height = sqrt(20^2 − 5^2) = sqrt(400 − 25) = sqrt(375) ≈ 19.36 feet.

Now the area is (1/2) × base × height = (1/2) × 10 × 19.36 ≈ 96.8 square feet. This rounds to about 97 square feet, matching the closest option. In practice, this is the typical way to estimate roof sections when you know the side lengths of the triangular end.