Frustum Pyramid Calculator
Calculator and formulas to calculate a frustum pyramid
This function calculates various parameters of a frustum pyramid. The frustum pyramid consists of a regular frustum or truncated pyramid and a pyramid placed on the larger base.
To calculate, enter the side lengths a and b, the heights of the pyramid and the frustum (truncated pyramid) and the number of corners. Then click on the 'Calculate' button.
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Frustum Pyramid Formulas
Overall height (\(\small{h}\))
\(\displaystyle h=i+j \)
Base perimeter (\(\small{P}\))
\(\displaystyle P =b\cdot n\)
Base area (\(\small{A}\))
\(\displaystyle A = \frac{ n · a^2 }{ 4 · tan(\frac{π}{n})} \)
Lateral surface frustum (\(\small{L_F}\))
\(\displaystyle L_F = \frac{n}{4} \cdot (a + b) \cdot \sqrt{cot^2\left(\frac{π}{n}\right) \cdot (a - b)^2 + 4\cdot i^2 } \)
Surface pyramid (\(\small{L_P}\))
\(\displaystyle L_P = n · b · \frac{\sqrt{j^2 + \frac{1}{4} · b^2 · cot^2(\frac{π}{n})}}{2} \)
Entire surface (\(\small{S}\))
\(\displaystyle S = A+ L_F+L_P \)
Volume Frustum (\(\small{V_F}\))
\(\displaystyle V_F = \frac{i}{3} · \left(\frac{n · (a^2 + b^2)}{4 · tan(\frac{π}{n})} \displaystyle + \sqrt{\frac{ n^2 · a^2 · b^2 }{ (4 · tan(\frac{π}{n}))^2}} \right) \)
Volume Pyramide (\(\small{V_P}\))
\(\displaystyle V_P = \frac{n · b^2 · j}{12 · tan(\frac{π}{n})} \)
Volume (\(\small{V}\))
\(\displaystyle V = V_F+V_P \)
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