Find the lateral surface area of the triangular PRISM. Solve this problem by determining the area of the shapes net
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.