Find the lateral surface area of the triangular prism . Solve by determining the area of the shapes net . 14in 12 in 5 in 13in
To find the lateral surface area of the triangular prism, we first need to find the area of the net of the triangular prism.
The net of a triangular prism consists of two triangles and three rectangles.
The base of the triangles is the base of the triangular prism, which is 14in, and the height is 5in. The area of one triangle is (1/2) * base * height = (1/2) * 14 * 5 = 35in^2. Since there are two triangles, the total area of the triangles is 2 * 35 = 70in^2.
The lateral faces of the triangular prism are three rectangles. The base of each rectangle is the perimeter of one of the triangles, which is 14 + 12 + 13 = 39in. The height of the rectangles is the same as the height of the triangular prism, which is 5in. The area of each rectangle is base * height = 39 * 5 = 195in^2. Since there are three rectangles, the total area of the rectangles is 3 * 195 = 585in^2.
Therefore, the total area of the net of the triangular prism is 70in^2 + 585in^2 = 655in^2.
Since the lateral surface area of the triangular prism is the same as the area of the net, the lateral surface area of the triangular prism is 655in^2.