Question

A regular hexagonal pyramid whose base perimeter is 60cm has an altitude of 30cm. The volume of the pyramid is??

Answer 1

$altitude : \ H= 30 \ cm\\ \\ base \ perimeter = 60 \ cm\\ \\ P=6s \\ \\60=6s \ \ /:6\\ \\s=10 \ cm$

$Volume \ of \ a \ regular \ hexagonal \ pyramid \ is \ given \ by \\ \\ V = \frac{\sqrt{3}}{2}\cdot s^2\cdot h \\ where \ s \ is \ the \ side \ length \ of \ the \ hexagon \\ h \ is \ its \ height \\ \\ V=\frac{\sqrt{3}}{2}\cdot 10^2\cdot 30 = \sqrt{3}\cdot 100\cdot 15 =1500\sqrt{3} \ cm^3$