Question

Find the volume of the square pyramid shown. Round to the nearest tenth if necessary.

Answer 1

Formula
The formula for a pyramid is V = 1/3 * B * h

B = s * s of the square bottom
s = 10

B = 10*10
B = 100 square feet.

Height.
The height is not given. You find it using a^2 + b^2 = c^2
a = 1/2 length of the side of the base
b = height
c = 13^2

If you draw a line to the midpoint of the base form the base of the height, you get 5. You have to read that a couple of times. I don't know if you can see this or not. 
AC = 10
B is the midpoint of AC that means that BD = 5
BH = 13 Given
We need HD

Use the pythagorean theorem
HD^2 + BD^2 = BH
HD^2 + 5^2 = 13^2
HD^2 + 25 = 169
HD^2 = 169 - 25
HD^2 = 144 Take the sqrt of both sides.
HD = sqrt(144)
HD = 12

Find the Volume
V = 1/3 * B * H
V = 1/3 * 100 * 12
V = 1/3 * 1200
V = 400

Answer
V = 400 square feet <<< answer