The given figure shows a circle with centre O and a square ABCD. The radius of the circle is 14 cm.
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What is the area of the shaded region?
Dear Student,
area of shaded region
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
So
area of shaded region
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
So
Area of 4 sectors = Πr²
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
Regards