Question

Use the image to answer the question.%0D%0A%0D%0A%0D%0A%0D%0AFind the lateral surface area of the triangular prism. Solve this problem by determining the area of the shape’s net.%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A480 in.2%0D%0A480 in. squared%0D%0A%0D%0A564 in.2%0D%0A564 in. squared%0D%0A%0D%0A504 in.2%0D%0A504 in. squared%0D%0A%0D%0A420 in.2

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the lateral surface area of the triangular prism, we first need to find the area of the shape's net.

The net of the triangular prism consists of two congruent triangles for the top and bottom faces, and three rectangles for the lateral faces.

Each triangle has a base of 10 inches and a height of 8 inches. The area of each triangle is 1/2 * base * height = 1/2 * 10 * 8 = 40 in^2.

Each rectangle has a length of 10 inches and a height of 8 inches. The area of each rectangle is length * height = 10 * 8 = 80 in^2. Since there are three rectangles, the total area of the rectangles is 3 * 80 = 240 in^2.

Therefore, the total area of the net of the triangular prism is 2 * 40 + 240 = 80 + 240 = 320 in^2.

Since the lateral surface area of the triangular prism is the same as the total area of the net, the lateral surface area is 320 in^2.

So, the correct answer is:

320 in^2