Question

The base of a prism is a right angled triangle with legs $6$cm, $8$cm and hypotenuse $10$cm. If the total surface area of the prism is $156c{m}^2$, find its height and its lateral surface area.

Answer 1

Given: the base is a right angled triangle with sides $a=6$cm, $b=8$cm, $c=10$cm and T.S.A$=156c{m}^2$. We know that
T.S.A.$=2B+Ph=2\times \frac{1}{2}\times 8\times 6+(6+8+10)h=48+24h$.
Thus $48+24h=156$. This implies that $24h=156-48=108$.
Hence $h=\frac{108}{24}=4.5$cm.
Therefore LSA$=Ph=(6+8+10)\times 4.5=24\times 4.5=108c{m}^2$.