To find the lateral surface area of the triangular prism, we first need to find the area of the net of the prism. The net of a prism is the 2D shape that can be folded to create the 3D shape of the prism.
In the case of a triangular prism, the net consists of two triangles (the bases of the prism) and three rectangles (the lateral faces of the prism). Let's assume the base of the triangle is b and the height of the triangle is h. The base of the prism is a rectangle with base b and height h. The lateral faces are three rectangles with base b and height x, where x is the height of the prism.
The area of the net can be calculated as follows:
Area of two triangles = 2 * (1/2 * b * h) = b * h
Area of three rectangles = 3 * (b * x) = 3bx
Total area of the net = b h + 3bx
Now, we can calculate the lateral surface area of the prism by considering the three lateral faces. Since the lateral faces are rectangles, the lateral surface area is 3 times the base times the height of one of the lateral faces:
Lateral Surface Area = 3 * b * x
Therefore, the lateral surface area of the triangular prism is 3bx.
Find the lateral surface area of the triangular PRISM. Solve this problem by determining the area of the shapes net
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