Regular Polygon Frustum Calculator

About the Regular Polygon Frustum

A frustum of a regular pyramid is formed by cutting off the top of a regular pyramid parallel to its base. The frustum has two parallel bases that are regular polygons with the same number of sides.

Formulas Used:

Area of upper base (\(A_1\)): \[ A_1 = \frac{1}{4} n a^2 \cot\left(\frac{180^{\circ}}{n}\right) \]

Area of lower base (\(A_2\)): \[ A_2 = \frac{1}{4} n b^2 \cot\left(\frac{180^{\circ}}{n}\right) \]

Volume (\(V\)): \[ V = \frac{1}{3} h (A_1 + A_2 + \sqrt{A_1 A_2}) \]

Lateral Surface Area (\(A_L\)): \[ A_L = \frac{1}{2} n (a + b) H \] where \(H\) is the slant height

\[ \text{Total Surface Area:} \; A_T = A_1 + A_2 + A_L \] where \[ H^2 = c^2 - \left(\dfrac{b-a}{2}\right)^2 \] \[ c^2 = h^2 + (r_2-r_1)^2 \] \[ r_1 = \dfrac{a}{2 \sin(\alpha/2)} \quad \text{and} \quad r_2 = \dfrac{b}{2 \sin(\alpha/2)}\] \[ \alpha = \dfrac{360^{\circ}}{n} \]

Note: All angles are in degrees, lengths in any unit, areas in square units, volume in cubic units.