The side length of square ABCD is 14 , cm. As | vedclass

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(A) The side length of the square $ABCD$ is $s = 14 \, cm$.The area of the square $ABCD = s^2 = 14^2 = 196 \, cm^2$.Each vertex of the square is the c

Vedclass · Accepted Answer

$42$

Vedclass · Answer

(A) The side length of the square $ABCD$ is $s = 14 \, cm$.The area of the square $ABCD = s^2 = 14^2 = 196 \, cm^2$.Each vertex of the square is the centre of a circle with radius $r = 7 \, cm$.Inside the square,there are four sectors,each with a central angle of $90^\circ$ (since it is a square).The sum of the areas of these four sectors is $4 	imes (\frac{90}{360} 	imes \pi r^2) = \pi r^2$.Substituting $r = 7 \, cm$,the area of the four sectors $= \frac{22}{7} 	imes 7 	imes 7 = 154 \, cm^2$.The area of the shaded region = (Area of square) - (Sum of areas of four sectors).Area of shaded region $= 196 - 154 = 42 \, cm^2$.

The side length of square $ABCD$ is $14 \, cm$. As shown in the diagram,circles with radius $7 \, cm$ are drawn with each vertex as the centre so that each circle touches two other circles externally. Find the area of the shaded region in $cm^2$.

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