Show that the volume of a pyramid of height h whose base is an equilateral triangle o

**derrickd** · December 3rd 2008, 09:28 PM

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)

**Shyam** · December 3rd 2008, 09:43 PM

Originally Posted by derrickd

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)

For, equilateral triangle of base,

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

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

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

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