Question

The lateral surface area of a triangular prism is $240$ cm${}^2$ and its base is an equilateral triangle of side $10$ cm. What will be its total surface area?

Answer 1

Total Surface Area $=$ Lateral Surface Area $+$ Area of $2$ triangular sides.

Side of equilateral triangle $=s=10$ cm
$\therefore$ Area of the triangle $=\frac{\sqrt[2]{23}}{4}\times s^2$
$=\frac{\sqrt[2]{23}}{4}\times {10}^2$
$=\frac{\sqrt[2]{23}}{4}\times 100$
$=\sqrt[2]{23}\times 25$
$=1.732\times 25=43.3$ cm${}^2$

Therefore the area of two triangles $=43.3+43.3=86.6$ cm${}^2$

Thus total surface area $=240+86.6=326.6$ cm${}^2$