Pyramid Frustum Calculation

This function calculates the properties of a regular pyramid frustum".

To perform the calculation, enter the base and top length, height and number of vertices of the pyramid. Then click the 'Calculate' button.

Pyramid Frustum" Calculator  Input Delete Entries Base side length a Top side length b Height h Base vertices n Decimal places 0 1 2 3 4 6 8 10  Results Slant height s Edge length e Slant area As Lateral Surface AL Surface area S Perimeter P Volume V

Pyramid Frustum Formulas

Slant height

\(\displaystyle s= \sqrt{\frac{1}{4} · cot^2\left(\frac{π}{n} \right) · ( a - b )^2 + h^2} \)

Edge length

\(\displaystyle e =\sqrt{\frac{4 · s^2 + ( a - b )^2 }{4}}\)

Base and top area

\(\displaystyle A = n · \frac{a^2 + b^2}{4 · tan(\frac{π}{n})} \)

Slant area

\(\displaystyle A_s = \frac{(a + b) · s}{2} \)

Lateral Surface

\(\displaystyle A_m = n · A_s \)

Surface

\(\displaystyle S = A+ A_m \)

Perimeter

\(\displaystyle P = n ·a \)

Volume

\(\displaystyle V = \frac{h}{3} · \left( \frac{n ·( a^2 + b^2) }{ 4 · tan(\frac{π}{n})} + \sqrt{\frac{n^2 · a^2 · b^2}{(4 · tan(\frac{π}{n}))^2}} \right) \)