Find the area of the shaded region of the given figure, where ABCD is a square side 7 cm and sectors of radius 2.1 cm each are drawn at its four vertices.  Use   π = 22 7

Dear Student,

From the given figure, the area of shaded portion is given by,    Area of four circles each with radius 2.1 cm-area of four sectors each with radius 2.1 cmIt can be seen that the center of each circle lie at the vertex of square. So each of the sector is a quadrant of a circle.Therefore, the four sectors forms the four quadrant of a circle. So the combined area of four sectors is area of a single circle with radius 2.1 cm.Thus, the required area of shaded portion is,     =4×πr2-1×πr2     =4πr2-πr2     =3πr2     =3×227×2.1×2.1     =3×22×0.3×2.1     =41.58  cm2


Regards

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Area of shadedegion =area of 4 circle- area of 4 sector
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