Surface Area Unit Test
14 of 17 14 of 17 Items
Question
A “wet floor” warning sign is in the shape of a triangular pyramid without a base. The edge length of the base equilateral triangle is 15 inches, the height of the base triangle is 13 inches, and the height of the triangular faces is 18 inches. How much fabric is needed to make the sign given the base does not need fabric?(1 point)
Responses
502.5 in.2
502.5 in. squared
351 in.2
351 in. squared
405 in.2
405 in. squared
292.5 in.2
To find the total surface area of the triangular pyramid, we need to find the area of each triangular face and the area of the three lateral faces.
1. The area of each triangular face is 1/2 base x height.
Area = 1/2 x 15 in x 18 in = 135 in^2 (for each triangular face)
2. The area of the three lateral faces is 3 times the area of one triangular face.
Total lateral faces area = 3 x 135 in^2 = 405 in^2
3. The total surface area is the sum of the lateral faces area and the base area (which is not needed in this case).
Total surface area = 405 in^2 + 0 in^2 = 405 in^2
Therefore, the correct answer is 405 in^2.
351 in^2, 502.5 in^2, and 292.5 in^2 are not the correct answers.