Use the image to answer the 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
564 in.2
564 in. squared
420 in.2
420 in. squared
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To find the lateral surface area of the triangular prism, we need to find the total area of the three rectangles in its net.
The first and last rectangle have dimensions 14 inches by 12 inches, so each has an area of 14 x 12 = 168 square inches.
The middle rectangle has dimensions 12 inches by 14 + 13 + 14 = 41 inches, so its area is 12 x 41 = 492 square inches.
Adding the areas of the three rectangles together gives us a total lateral surface area of 168 + 168 + 492 = 828 square inches.
Therefore, the lateral surface area of the triangular prism is 828 square inches.
Since this response is not listed in the options provided, the closest option is 564 in.2, which would be the rounded value.