Use the image to answer the question.

Question

An illustration shows two views of a triangular prism.
The first view shows a 3-dimensional triangular prism with the highlighted rectangular base labeled as 14 inches in length and 12 inches in width. A right triangular side is labeled 5 inches in perpendicular height and is denoted by a right angle symbol at each end where the base and side meet. A hypotenuse is labeled as 13 inches. Edges that are not visible are drawn in dashed lines. The unfolded version shows three adjacent vertical rectangles where the first and the last are similar and the middle rectangle is bigger. The left rectangle is labeled 14 inches in vertical length. Two right triangles are adjoined on the top and bottom of the middle rectangle. The triangle base, which is also the width of the middle rectangle, is labeled as 12 inches. The hypotenuse of the triangle is 13 inches. The height of the right angle side of the triangle is labeled as 5.

Find the lateral surface area of the triangular prism. Solve this problem by determining the area of the shape’s net.

(1 point)
Responses

504 in.2
504 in. squared

480 in.2
480 in. squared

420 in.2
420 in. squared

564 in.2

Answer 1

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

The net of the triangular prism is made up of 3 rectangles: one rectangle with dimensions 14 inches by 12 inches, and two identical rectangles with dimensions 12 inches by 5 inches (since they correspond to the height of the triangular side).

The lateral surface area is the sum of the areas of the three rectangles:
14*12 + 2(12*5) = 168 + 2(60) = 168 + 120 = 288

Therefore, the lateral surface area of the triangular prism is 288 square inches.

None of the provided responses match this calculation, so none of the given options are correct.