The following figure shows a square card-board ABCD of side 28 cm. Four identical circles of largest possible size are cut from this card as shown below.

Find the area of the remaining card-board.

Given:

Side of square ABCD = 28 cm

Side of square = 2 x diameter of circle

Diameter of circle = $\dfrac{28}{2}$ = 14 cm

Radius of circle = $\dfrac{d}{2}$ = $\dfrac{14}{2}$ = 7 cm

Area of the remaining card-board = Area of square - 4 x Area of 1 circle

= side² - 4 x πr²

$= 28^2 - 4 \times \dfrac{22}{7} \times 7^2\\[1em] = 28^2 - 4 \times \dfrac{22}{7} \times 7 \times 7\\[1em] = 28^2 - 4 \times \dfrac{22}{\cancel{7}} \times \cancel{7} \times 7\\[1em] = 28^2 - 4 \times 22 \times 7\\[1em] = 784 - 616\\[1em] = 168 \text{ cm}^2$

Hence, the area of remaining cardboard is 168 cm².