Right prism with a rhombus base

Text

A right prism has height $10$ cm and a rhombus base whose diagonals are $12$ cm and $16$ cm. Find the lateral surface, the total surface and the volume.

Solution

The rhombus side is $\sqrt{6^2+8^2}=10$ cm; the base area is $\dfrac{12\cdot16}{2}=96$ cm$^2$ and the perimeter is $4\cdot10=40$ cm. Lateral surface: $S_\ell=40\cdot10=400$ cm$^2$. Total surface: $S_t=400+2\cdot96=592$ cm$^2$. Volume: $V=96\cdot10=960$ cm$^3$. $\boxed{S_\ell=400;\ S_t=592\ \text{cm}^2;\ V=960\ \text{cm}^3}$