From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in figure. Find the area of the remaining portion of the square.

The area of the whole square ABCD \( = \ 4^2 \ = \ 16 \)cm²

The sum of the area of the four quadrants at the four corners of the square

= The area of a circle of radius 1 cm

\(= \ \frac{22}{7} \ × \ 1^2 \ = \ \frac{22}{7} \)cm²

The area of the circle of diameter 2 cm, i.e., radius 1cm

\( = \ \frac{22}{7} \ × \ 1^2 \ = \ \frac{22}{7} \) cm²

\(\therefore \).Area of the remaining portion = The Area of the square ABCD - sum of the areas of the 4 quadrants - Area of the circle

\(= \ 16 \ - \ \frac{22}{7} \ - \ \frac{22}{7} \ = \ \frac{112 \ - \ 22 \ - \ 22}{7} \)

\( = \ \frac{68}{7} \)cm²