The figure below is a net for a triangular prism. Side a = 48 inches, side b = 10 inches, side c = 33 inches, and altitude d = 23 inches. What is the surface area of this figure?
First, we need to find the area of each of the five faces of the triangular prism.
Face 1: This is a rectangle with sides of 48 inches and 23 inches. The area is 48 x 23 = 1,104 square inches.
Face 2: This is another rectangle with sides of 10 inches and 23 inches. The area is 10 x 23 = 230 square inches.
Faces 3, 4, and 5: These are all congruent triangles with base 48 inches and height 33 inches (which is also the slant height of the triangle). The area of each triangle is (1/2)bh = (1/2)(48)(33) = 792 square inches. Since there are three of these faces, we multiply by 3 to get a total area of 2,376 square inches.
Now we can add up the areas of all five faces:
1,104 + 230 + 2,376 = 3,710 square inches
Therefore, the surface area of the triangular prism is 3,710 square inches.