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 $\displaystyle = \sqrt{s^2-\left(\frac{s}{2}\right)^2}=\frac{s\sqrt{3}}{2}$
Area of equilateral triangle (base) $\displaystyle A= \frac{s\times \frac{s\sqrt{3}}{2}}{2}=\frac{s^2\sqrt{3}}{4}$
Volume=$\displaystyle \frac{A\times h}{3}=\frac{\frac{s^2\sqrt{3}}{4}h}{3}=\frac{hs^2\ sqrt{3}}{12}$