Question

The perimeter of a regular triangle based prism is $18$m and its height is $13$m. Find its lateral and total surface area.

Answer 1

$\tan 30°=\frac{l}{3}$

$l=\sqrt{3}$

Slant height$=\sqrt{h^2+l^2}$

$=\sqrt{169+3}$

$=\sqrt{172}=2\sqrt{43}$

Lateral S.A$=(\frac{1}{2}\times base\times slantheight)\times 3$

$=3\times \frac{1}{2}\times 6\times 2\sqrt{43}$

$=18\sqrt{43}c{m}^3$

Total S.A. $=18\sqrt{43}+Ar.of△$

$=18\sqrt{43}+\frac{\sqrt{3}}{4}\times {\left(6\right)}^2$

$=(18\sqrt{43}+9\sqrt{3})c{m}^2$