The side length of square ABCD shown in the d | vedclass

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Question

(A) The side of the square $ABCD$ is $a = 42 \ cm$.Area of the square $ABCD = a^2 = 42^2 = 1764 \ cm^2$.There are four semicircles drawn on the sides

Vedclass · Accepted Answer

$1008$

Vedclass · Answer

(A) The side of the square $ABCD$ is $a = 42 \ cm$.Area of the square $ABCD = a^2 = 42^2 = 1764 \ cm^2$.There are four semicircles drawn on the sides of the square,each with a diameter equal to the side of the square,$d = 42 \ cm$. Therefore,the radius $r = 21 \ cm$.The area of the four semicircles is $4 	imes (\frac{1}{2} \pi r^2) = 2 \pi r^2$.Area $= 2 	imes \frac{22}{7} 	imes 21 	imes 21 = 2 	imes 22 	imes 3 	imes 21 = 2772 \ cm^2$.The shaded area is the area of the four semicircles minus the area of the square,as the overlapping regions are counted twice.Shaded Area $= 2772 - 1764 = 1008 \ cm^2$.

The side length of square $ABCD$ shown in the diagram is $42 \ cm$. The shaded design is formed by drawing semicircles on all the sides of the square. Find the area of the shaded design in $cm^2$.

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