Area and Volume of a Pyramid Area and Volume of a Pyramid


Instructions: Enter the side \(l\) and the height \(h\) of a square pyramid and the units (cm, mt, ft, etc) and the solver will compute the corresponding surface area and volume of the given square pyramid.


Type the side of the side of the base \(l\) =


Type the height of the pyramid \(h\) =




More About the Pyramid

In order to compute the surface area and volume of square pyramid with side \(l\) and height \(h\) we use the following formulas:

\[ \text{Area} = l^2 + 2l\sqrt{\frac{l^2}{4} + h^2}\] \[ \text{Volume} = \frac{l^2 h}{3} \]

Computationally speaking, it is quite simple to compute the surface area and the volume of a square pyramid, by simply plugging the side \(l\) and height \(h\) in the above formulas. For example, if the side is \(l = 3\) and the height is \(h = 4\), we compute

\[ \text{Area} = l^2 + 2l\sqrt{\frac{l^2}{4} + h^2} = 3^2 + 2\cdot 3\sqrt{\frac{3^2}{4} + 4^2} = 34.632 \] \[ \text{Volume} = \frac{l^2 h}{3} = \frac{3^2\cdot 4}{3} = 12 \]

which completes the calculation.

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