How to Calculate the Volume of a Square Pyramid

By Kat Walcott
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A square pyramid is a geometric figure with a square base and four, triangular sides that meet at a common vertex. After determining the height of the figure and the area of its base, find the volume using a formula made up of basic multiplication and division.

Area of the Base of a Square Pyramid

If the area of the base and the height of the figure is not provided, you need to determine what they are before you can calculate the volume. To find the area of the base, square the length of the sides of the base. If the length of the base is 5, your equation would be five squared equals 25. Written out, it should look like this: 5^2=25. Therefore, the area of the base is 25.

Height of a Square Pyramid

For height, you will need the slant length and half-length of the base. Slant length is the length from the base to top of the pyramid and the half-length of the base is the base length divided by two. Since the base length is 5, calculate five divided by two to get 2.5. For this example, the slant length will be 18. To find the height, calculate the square root of 18 squared minus 2.5 squared to get a height of 17.8. Written out it will be: sqrt[18^2 - 2.5^2] = 17.8. Round up your answer to get 18 as the height.

Volume of a Square Pyramid

To determine the volume, you will need to plug your base area and height values into a formula -- height times area of the base divided by three. Using our values, the equation would be 18 times 25, divided by three, to equal 150. Written out, your equation should look like this: 18 x 25 / 3 = 150.Therefore, the volume of the square pyramid is 150.