In the given figure, ABCD is a square of side 14 cm. With centers A, B, C and D, four circles are drawn such that each circle touches externally two of the remaining three circles. Find the area of the shaded region.

Asked by Pragya Singh | 1 year ago |  60

##### Solution :-

Side of square = 14 cm

Four quadrants are included in the four sides of the square.

Radius of the circles = $$\dfrac{14}{2}$$ cm = 7 cm

Area of the square ABCD = 14= 196 cm2

Area of the quadrant = $$\dfrac{πR^2}{4}$$ cm2 = ($$\dfrac{22}{7}$$) ×$$\dfrac{7^2}{4}$$ cm2

$$\dfrac{77}{2}$$ cm2

Total area of the quadrant = 4×$$\dfrac{77}{2}$$ cm= 154cm2

Area of the shaded region = Area of the square ABCD – Area of the quadrant

= 196 cm– 154 cm2

= 42 cm2

Answered by Abhisek | 1 year ago

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