# ACT Math : How to find the length of an edge of a pyramid

## Example Questions

### Example Question #1 : How To Find The Length Of An Edge Of A Pyramid

A square pyramid has a volume of  and a height of . What is the perimeter of the base of the pyramid?

Explanation:

The formula for the volume of a pyramid is:

We know that  and ; however, this still leaves us with two variables in the equation:  and . By definition, a square pyramid's base has sides of equal length, meaning that  and  are the same. Therefore, we can substitute  for , or .

This gives us a new equation of:

We then plug in the variables we know:

Multiply both sides by 3:

Divide both sides by 9:

Therefore, we now know that the length of the pyramid's base is . The question, however, asks for the perimeter of the pyramid's base. Since all of the sides of the base are the same, they must all be . So we multiply . Therefore, the perimeter of the pyramid's base is .

### Example Question #2 : How To Find The Length Of An Edge Of A Pyramid

A square pyramid has a slant height of 8. The edge of a face is 12. What is the measure of an edge of its base?