Rectangular Pyramid Calculator

Name: Rectangular Pyramid - Geometry Calculator
Author: Jürgen Kummer

Calculations for a rectangular pyramid. This is a straight pyramid with a rectangle as the base. The four lateral faces are isosceles triangles, two opposite faces with base a and legs c, and two opposite faces with base b and legs c.
Enter the two side lengths a and b, as well as the height h. Choose the number of decimal places, then click Calculate.

Formulas:

c = \sqrt{h^{2} + {(\frac{a}{2})}^{2} + {(\frac{b}{2})}^{2}}

s_{1} = \sqrt{h^{2} + {(\frac{b}{2})}^{2}}

s_{2} = \sqrt{h^{2} + {(\frac{a}{2})}^{2}}

A = a b + a \cdot s_{1} + b \cdot s_{2}

V = \frac{1}{3} \cdot a b h

Lengths, width and heights have the same unit (e.g. meter), the area has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit ^-1.

The rectangular pyramid is a special case of the general pyramid. If the apex of a rectangular pyramid is cut off straight across, a rectangular frustum is formed. This form of truncated pyramid is probably at least as common as the according pyramid. Some Nubian pyramids have a rectangular base. This shape is also found for roofs and tents.

The two slant heights can be calculated using the Pythagorean theorem. They correspond to the hypotenuses of the right triangles with legs h and a/2, and b/2, respectively. The length of the slanted edges corresponds to the space diagonal of a cuboid with three edges h, a/2, and b/2. The corresponding formula is also known as the three-dimensional Pythagorean theorem. The surface area is calculated as the area of the rectangle at base ab and the four lateral triangles. The two triangles with base a and height s₁ together have the same area as a rectangle a times s₁. The same applies to the two triangles with base b and height s₂. The volume is calculated using the volume formula for the general pyramid.

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