Show that the volume of a pyramid of height h whose base is an equilateral triangle of side s is equal to

{(√3)(h)(s^2)}

(12)

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- Dec 3rd 2008, 09:28 PMderrickdShow that the volume of a pyramid of height h whose base is an equilateral triangle o
Show that the volume of a pyramid of height h whose base is an equilateral triangle of side s is equal to

__{(√3)(h)(s^2)}__

(12) - Dec 3rd 2008, 09:43 PMShyam
For, equilateral triangle of base,

height of equilateral triangle $\displaystyle = \sqrt{s^2-\left(\frac{s}{2}\right)^2}=\frac{s\sqrt{3}}{2}$

Area of equilateral triangle (base) $\displaystyle A= \frac{s\times \frac{s\sqrt{3}}{2}}{2}=\frac{s^2\sqrt{3}}{4}$

Volume=$\displaystyle \frac{A\times h}{3}=\frac{\frac{s^2\sqrt{3}}{4}h}{3}=\frac{hs^2\ sqrt{3}}{12}$