# 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:      $$V = \dfrac{1}{3} H \times A_b = \dfrac{L W H}{3}$$
Lenght of Edge TA = Lenght of Edge TB = Lenght of Edge TC = Lenght 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 "enter". The outputs are all parameters defined above
 Length L = 8 , Width W = 6 , Height H = 12 Slant height TO':      $$H'=$$ Slant height TO'':      $$H''=$$ Area of rectangular base ABCD:      $$A_b =$$ = Area of triangle DTC: $$A_{DTC}$$ = Area of triangle ATD: $$A_{ATD}$$ = Total Area of Surface of Pyramid: $$A_T =$$ = Volume of Pyramid: $$V =$$ Lenght of Edge: $$S =$$ Angle DTC = Angle ATB: $$\alpha =$$ degrees Angle ATD = Angle BTC: $$\beta =$$ degrees

## Dimensions and Net Needed to Make a Pyramid

The net of a pyramid with rectangular base is shown below. The length $$L$$ and width $$W$$ are given and the heights $$H'$$ and $$H''$$ are calculated using the above calculator. Triangles ADT and BCT are congruent and triangles CDT and BAT are also congruent.

## More References and Links to Geometry Calculators

Online Geometry Calculators and Solvers.