Find the area of the shaded region in the fig | vedclass

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(C) Given,side of square $ABCD = 12 \, cm$.Since $P, Q, R, S$ are mid-points of sides $AB, BC, CD, DA$ respectively,the radius of each quadrant arc is

Vedclass · Accepted Answer

$30.96$

Vedclass · Answer

(C) Given,side of square $ABCD = 12 \, cm$.Since $P, Q, R, S$ are mid-points of sides $AB, BC, CD, DA$ respectively,the radius of each quadrant arc is $r = \frac{12}{2} = 6 \, cm$.Area of one quadrant = $\frac{1}{4} \pi r^{2} = \frac{1}{4} 	imes 3.14 	imes (6)^{2} = \frac{3.14 	imes 36}{4} = 3.14 	imes 9 = 28.26 \, cm^{2}$.Area of four such quadrants = $4 	imes 28.26 = 113.04 \, cm^{2}$.Area of square $ABCD = (side)^{2} = (12)^{2} = 144 \, cm^{2}$.Area of the shaded region = Area of square $ABCD - $ Area of four quadrants.Area of the shaded region = $144 - 113.04 = 30.96 \, cm^{2}$.

Find the area of the shaded region in the figure where arcs drawn with centers $A, B, C,$ and $D$ intersect in pairs at mid-points $P, Q, R,$ and $S$ of the sides $AB, BC, CD,$ and $DA,$ respectively of a square $ABCD$ (Use $\pi = 3.14$) (in $cm^{2}$).

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