# Rectangular Pyramid Calculator and Maker

Online calculator to calculate the slant heights, surface area, the volume and many other parameters of a pyramid given the dimensions of its **rectangular** base and its height. The calculator gives all parameters necessary to make a pyramid with a rectangualr base. The net of the pyramid with all parameters to make it is shown at the bottom of the page.

## Formulas of Area and Volume of the Pyramid Used in this Calculator

Let \( L \), \( W \) be the dimensions of a rectangular base of a pyramid and \( H \) its height.Area of rectangular base ABCD: \( A_b = L \times W \)

Slant height TO': \( H'= \sqrt{H^2+(L/2)^2} \) (length of TO' which is the altitude of triangle DTC )

Slant height TO'': \( H'' = \sqrt{H^2+(W/2)^2} \) (length of TO'' which is the altitude of triangle ATD )

Area of triangle (Face) DTC: \( A_{DTC} = \dfrac{1}{2} H' \times W \)

Area of triangle (Face) ATD: \( A_{ATD} = \dfrac{1}{2} H'' \times L \)

Total Area of Pyramid: \( A_T = A_b + 2 \times A_{DTC} + 2 \times A_{ATD} \) (area of base + twice area of triangle DTC + twice the area of triangle ATD)

Volume of Pyramid: \( V = \dfrac{1}{3} H \times A_b = \dfrac{L W H}{3}\)

Length of Edge TA = Length of Edge TB = Length of Edge TC = Length of Edge TD: \( S = \sqrt{H^2 + (W/2)^2 + (L/2)^2 } \)

Angle DTC = Angle ATB: \( \alpha = 2 \arcsin {\dfrac{W/2}{S}} \)

Angle ATD = Angle BTC: \( \beta = 2 \arcsin{\dfrac{L/2}{S}} \)

## How to Use the Pyramid Calculator

Enter the length L and width W of the base of the pyramid and H the height of the pyramid as positive real numbers and press "calculate". The outputs are all parameters defined above