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# 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.

Answer :

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