Think of this shape as two pyramids joined together. Find the area of one of the pyramids and multiply by 2.
Volume of pyramid = area of base * height * 1/3
The base is a square with sides of 10 cm. The area of the base is 100 square cm.
Use the pythagorean theorem to find the height.
a^2 + b^2 = c^2
a is half the length of one of the sides, a = 5
c is the length of one of the sides, c = 10
b is the height of the pyramid. solve for b
5^2 + b^2 = 10^2
25 + b^2 = 100
b^2 = 75
b = sqrt(75)
b = 5 * sqrt(3)
Volume of the pyramid = area of base * height
V = 100 * 5 * sqrt(3)
V = 500 * sqrt(3)
This is the volume of one of the pyramids. Multiply this by 2.
1000 * sqrt(3)
1732.05 cubic cm