Question

A square sheet of 2 cm is cut from each corner of a rectangular piece of aluminium sheet of length 12 cm and breadth 8 cm. Find the area of the left over aluminium sheet.

Answer 1

We have,
Side of each square sheet cut from each corner = 2 cm,
Length of the rectangular piece of sheet = 12 cm and
Breadth of the rectangular piece of sheet = 8 cm

$$\begin{gathered} \mathrm{As},\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{each}\mathrm{square}=\mathrm{Side}\times \mathrm{Side} \\ =2\times 2 \\ =4{\mathrm{cm}}^2 \\ \mathrm{So},\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{four}\mathrm{square}\mathrm{sheets}=4\times 4=16{\mathrm{cm}}^2 \\ \mathrm{Also},\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{rectangular}\mathrm{sheet}=\mathrm{Length}\times \mathrm{Breadth} \\ =12\times 8 \\ =96{\mathrm{cm}}^2 \\ \mathrm{Now},\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{sheet}\mathrm{left}\mathrm{over}=\mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{rectangular}\mathrm{sheet}-\mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{square}\mathrm{sheet} \\ =96-16 \\ =80{\mathrm{cm}}^2 \end{gathered}$$

So, the area of the left over aluminium sheet is 80 cm².