Geometry! Cannot find surface area without slant height?

Question

A problem shows a right regular pyramid with the perimeter of the base and the height from the apex of the pyramid to the center of the base given. Lucy, who is asked to find the surface area of the pyramid, says that she can't because she doesn't know the slant height. How should you respond?

Answer 1

Draw and label a diagram!

1. divide the perimeter by 4. The result is the length of one side

2. divide the length of a side by 2. The results is the length of the short left of a right triangle

3. the height is the long leg of a right triangle

4. use Pythagoras to calculate the length of the hypotenuse (slant height)

5. determine the surface area.