Right prism with an isosceles-triangle base

Text

A right prism has as base an isosceles triangle with base $16$ cm and equal sides $10$ cm; the prism height is $12$ cm. Find the total surface area and the volume.

Solution

The base triangle’s height is $\sqrt{10^2-8^2}=6$; the base area is $\dfrac12\cdot16\cdot6=48$ cm$^2$ and the perimeter is $16+10+10=36$ cm. Lateral surface: $36\cdot12=432$; total surface: $S_t=432+2\cdot48=528$ cm$^2$. Volume: $V=48\cdot12=576$ cm$^3$. $\boxed{S_t=528\ \text{cm}^2;\ V=576\ \text{cm}^3}$