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प्रश्न
Four equal circles are described about the four corners of a square so that each touches two of the others, as shown in the figure. Find the area of the shaded region, if each side of the square measures 14 cm.
उत्तर
Side of the square = 14 cm
Radius of the circle `=14/2 = 7 "cm"`
Area of the quadrant of one circle` = 1/4pi"r"^2`
`=1/4xx22/7xx7xx7`
= 38.5 cm2
Area of the quadrants of four circles = 38.5 × 4 = 154 cm2
Now,
Area of the square =(Side)2
= 142
= 196 cm2
Area of the shaded region = Area of the square -- Area of the quadrants of four circles
= 196 - 154
= 42 cm2
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