Find the lateral surface area of the triangular prism. Solve this
problem by determining the area of the shape’s net.
(1 point)
504 in.
2
564 in.
2
420 in.
2
480 in.
2
To find the lateral surface area of the triangular prism, we first need to find the net of the shape. The net of a triangular prism consists of two congruent triangles and three rectangles.
The lateral surface area is the sum of the areas of the five faces of the net.
The area of each triangle is 1/2 * base * height. Since the base of the triangle is the same as the base of the prism, the base is equal to 12 inches and the height is 16 inches (height of the prism).
Area of each triangle = 1/2 * 12 * 16 = 96 in^2
Since there are two congruent triangles, their total area is 2 * 96 = 192 in^2
The area of each rectangle is length * width. The length of the rectangles is the same as the height of the prism (16 inches) and the width is the same as the length of the base of the prism (10 inches).
Area of each rectangle = 10 * 16 = 160 in^2
Since there are three rectangles, their total area is 3 * 160 = 480 in^2
Therefore, the lateral surface area of the triangular prism, which is the sum of the areas of the triangles and rectangles, is 192 + 480 = 672 in^2.
The lateral surface area of the triangular prism is 672 in^2.