The bottom shape is a cube with base edges of 16 meters. The top shape is a right pyramid with a height of 15 meters. What is the surface area of this composite figure?

Question

ranga · Answer

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For the cube portion, there will be 4 exposed squares that will be part of the lateral surface area. So find the area of one square of length 16m and multiply it by 4 to get the lateral surface area of the cube.

For the 4 triangles that are part of the pyramid, first find the height of the triangle. 
The height of the pyramid AB = 15m.  BC = half the length of the square = 16/2 = 8.
Find AC which will be the height of the triangle.

Find the area of one triangle using the formula:
Area of a triangle = 1/2 * base * height. 
Then multiply by 4 because there are four triangles in a pyramid. 

Add the surface areas of the cube and the triangles to find the total lateral surface area.