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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

420 in.2
420 in. squared

480 in.2
480 in. squared

564 in.2
564 in. squared

504 in.2
504 in. squared
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Answer 1

To find the lateral surface area of the triangular prism, we first need to calculate the areas of the individual shapes in the net. The net of the triangular prism consists of three rectangles and two right triangles.

The two rectangles on the left and right sides have a length of 14 inches and a width of 12 inches. The area of each rectangle is 14 x 12 = 168 square inches. Since there are two identical rectangles, the total area for these two rectangles is 168 x 2 = 336 square inches.

The middle rectangle has a length of 14 inches and a width of 12 inches. The area of the middle rectangle is 14 x 12 = 168 square inches.

The two right triangles have a base of 12 inches and a height of 5 inches. The area of one right triangle is 1/2 x base x height = 1/2 x 12 x 5 = 30 square inches. Since there are two identical triangles, the total area for these two triangles is 30 x 2 = 60 square inches.

Therefore, the total lateral surface area of the triangular prism is 336 + 168 + 60 = 564 square inches.

The correct answer is 564 in.2 or 564 in. squared.