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# Square Pyramid Calculator

Square pyramids were frequently used in ancient architecture and are one of the simplest shapes in solid geometry. The three main measures of a square pyramid are the base length **B**, height **H**, and triangular side length **S**. See figure below.

If you know any two of these measurements, you can compute the third. You can then compute the volume of the pyramid and the area of a triangular face once you know the values of B, H, and S. The equations are given below, or you may use the calculator at left.

### Relations Among B, S, and H

For a square pyramid with a base length of B and a height of H, you can compute S with the formulaS = sqrt(B²/2 + H²).

If you know B and S and want to find H, the formula is

H = sqrt(S² - B²/2).

And finally, the formula for B in terms of H and S is

B = sqrt(2S² - 2H²).

### Area of a Triangular Face

Each face of a square pyramid is an isosceles triangle with sides S, S, and B. Using Heron's formula for triangular area, you can derive the expressionArea = (B)sqrt(S²/4 - B²/16).

### Volume of a Square Pyramid

The three-dimensional volume of a square pyramid is given by the equationVolume = B²H/3.

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