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.
To find the lateral surface area of the triangular prism, we need to find the area of the net of the prism.
First, we need to find the area of the three rectangles that make up the net. The two smaller rectangles have dimensions of 12 inches by 14 inches, so their areas are:
2 * (12 inches * 14 inches) = 2 * 168 = 336 square inches
The larger rectangle has dimensions of 12 inches by 5 inches, so its area is:
12 inches * 5 inches = 60 square inches
Now, we need to find the area of the two right triangles on the net. The base of each triangle is 12 inches, and the height is 5 inches, so the area of each triangle is:
1/2 * (12 inches * 5 inches) = 1/2 * 60 = 30 square inches
Since there are two triangles, the total area of the triangles is 2 * 30 = 60 square inches
Adding all the areas together, we get:
336 square inches + 60 square inches + 60 square inches = 456 square inches
Therefore, the lateral surface area of the triangular prism is 456 square inches.