Question

The base of a right prism is a triangle whose sides are of lengths $9$ cm, $10$ cm, and $11$ cm. Height of the prism is $15$ cm. Find the volume (in cu. inches) of the prism.

Answer 1

Given : Sides of triangle $a=9cm,b=10cm,c=11cm$ Height of prism$\left(h\right)=15cm$

Semi-perimeter of a triangle$\left(s\right)=\frac{(9+10+11)}{2}=15$

Area of triangle $=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{15\left(6\right)\left(5\right)\left(2\right)}$

$=30\sqrt{2}c{m}^2$

Volume of prism $=Basearea\times height$

$=30\sqrt{2}\times 15$

$=636.3961cu.cm$

$=39cu.inches$