To find the lateral surface area of the triangular prism, we need to find the sum of the areas of the three rectangles labeled on the net.
The first rectangle has a length of 14 inches and a width of 12 inches, so its area is 14 * 12 = 168 in^2.
The second rectangle (with the right triangle on top and bottom) has a base of 12 inches and height of 5 inches, so its area is (12 * 5) / 2 + (12 * 5) / 2 = 30 + 30 = 60 in^2.
The third rectangle has the same dimensions as the first one, so its area is 168 in^2.
Adding the three areas together: 168 + 60 + 168 = 396 in^2.
Therefore, the lateral surface area of the triangular prism is 396 in^2.
None of the provided options match the correct answer, but the calculated answer is 396 in^2.
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
564 in.2
564 in. squared
504 in.2
504 in. squared
420 in.2
420 in. squared
480 in.2
480 in. squared
1 answer
1 answer