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 total surface area (in sq. inches) of the prism.

Answer 1

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

Perimeter of a triangle$\left(p\right)=(9+10+11)2=15$

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

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

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

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

Total surface area of the prism $=ph+2B$

$=450+84.84$

$=534.852c{m}^2$

$=82.9sq.inches$

Hence, the answer is $82.9sq.inches$