# A square pyramid with a height of 6 and a volume of 162. Can you find the base edge?

## I don't understand this math at all. and I'm failing a lot of classes and need to get my grade up!!!! can someone please help me!!!!. and my teacher makes us show work. so if you can possibly do that, if its no trouble. please show some work!! and idk if i have to draw anything. ill just draw a square pyramid and can you guys help me with the math.?

##### 1 Answer
Mar 1, 2017

The edges of the square base are all 9 units long.

#### Explanation:

The general formula for the volume of any pyramid is :

$V = \frac{1}{3} \text{area of base" xx "perpendicular height}$

In this case we have been told that the height is $\textcolor{b l u e}{6}$ and the volume is $\textcolor{red}{162}$.

$\frac{\text{Area} \times \textcolor{b l u e}{h}}{3} = \textcolor{red}{V}$

This means: ("Area" xx color(blue)(6))/3 =color(red)(162)" "larr  solve to find the area

$\text{Area} = \frac{3 \times 162}{6}$

$\text{Area of base} = 81$

We also know that the base is a square.

In a square: ${\text{Area = side}}^{2} = 81$

The side of the square is the edge of the square base.

"side = sqrt 81 = 9