Question

A cuboid has total surface area of 50 m² and lateral surface area is 30 m². Find the area of its base.

Answer 1

$$\begin{gathered} \mathrm{Total}\mathrm{sufrace}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cuboid}=50{\mathrm{m}}^2 \\ \mathrm{Its}\mathrm{lateral}\mathrm{surface}\mathrm{area}=30{\mathrm{m}}^2 \\ \mathrm{Now},\mathrm{total}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cuboid}=2\times (\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{base})+(\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}4\mathrm{walls}) \\ \Rightarrow 50=2\times (\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{base})+\left(30\right) \\ \Rightarrow 2\times (\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{base})=50-30=20 \\ \therefore \mathrm{Surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{base}=\frac{20}{2}=10{\mathrm{m}}^2 \end{gathered}$$