Question

Find the lateral surface area and total surface area of an equilateral triangle based prism with height $8$cm and base side $4$cm.

Answer 1

Given: $a=4$cm and $h=8$cm; to find L.S.A and T.S.A
We know L.S.A$=Ph=3\times a\times h=3\times 4\times 8=96c{m}^2$.
Further T.S.A$=2B+Ph=2\left(\frac{a^2}{4}\right)+3ah=\frac{\sqrt{3}}{2}{4}^2+96\approx (8\times 1.73)+96=109.84c{m}^2$.
Thus the total surface area is approximately $109.84c{m}^2$.