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

480 in.2

420 in.2

564 in.2

Answer 1

To find the lateral surface area of the triangular prism, we need to find the total area of all the sides excluding the bases.

First, we find the area of the two vertical rectangles:
- The area of each rectangle is 14 inches (vertical length) * 12 inches (width) = 168 square inches.
- Since there are two identical vertical rectangles, the total area for both is 168 square inches * 2 = 336 square inches.

Next, we find the area of the two right triangles:
- The area of each right triangle is 1/2 * base * height = 1/2 * 12 inches * 5 inches = 30 square inches.
- Since there are two identical right triangles, the total area for both is 30 square inches * 2 = 60 square inches.

Now, add the areas of the vertical rectangles and the right triangles:
336 square inches + 60 square inches = 396 square inches.

Therefore, the lateral surface area of the triangular prism is 396 square inches, which is not one of the provided answer choices. So the correct answer is not listed.