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The length of the ABCD square is14 cm, as shown in the figure. M.Each circle draws four congruentcircles centered on A, B, C andD, externally touching two of theremaining three circles. Shaded.Find the area of the part: |
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Answer» Given: Side of square ABCD = 14 cm Radius of circles with centers A, B, C and D = 14/2 = 7 cm Area of shaded region = Area of square - Area of four sectors subtending RIGHT angle Area of each of the 4 sectors is equal to each other and is a sector of 90° in a circle of 7 cm radius. So, Area of four sectors will be equal to Area of one complete circle Area of 4 sector = πr² 2*22/7 * 7 area of sector = 154cm² Area of square ABCD = (Side)² Area of square ABCD = (14)² Area of square ABCD = 196 cm² Area of shaded PORTION = Area of square ABCD - 4 × Area of each sector = 196 – 154 = 42 cm² Therefore, the area of shaded portion is 42 cm² |
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