Find the perimeter and area of the shaded region shown in the figure. The four corners are circle quadrants and at the centre, there is a circle.
Mensuration
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Question

Find the perimeter and area of the shaded region shown in the figure. The four corners are circle quadrants and at the centre, there is a circle.

KnowledgeBoat · Accepted Answer

4 quadrants = 1 full circle Circumference of circle = 2πr = 2 × 3.14 × 1 = 6.28 cm. Length of each shaded straight sides = 4 - 1 - 1 = 2 cm. Total length = 4 × 2 = 8 cm. Central circle boundary : radius = = 1 cm. Circumference of circle = 2πr = 2 × 3.14 × 1 = 6.28 cm. Total perimeter = 6.28 + 8 + 6.28 = 20.56 cm. Area of shaded region = Area of the square - (Area removed at the corners - Area of central circle) Area of square = (side)2 = 42 = 16 cm2. Area removed at the corners : Area of 1 quadrant = πr2 = × 3.14 × 12 = 0.785 ∴ For 4 quadrants = 4 × 0.785 = 3.14 cm2. Area of central circle = πr2 = 3.14 × 12 = 3.14 cm2. Area of shaded region = Area of square - Area of central circle - Area of 4 quadrants = 4 × 4 - (3.14 + 3.14) = 16 - 6.28 = 9.72 cm2. Hence, perimeter = 20.56 cm and area of shaded region = 9.72 cm2.

Mathematics

Find the perimeter and area of the shaded region shown in the figure. The four corners are circle quadrants and at the centre, there is a circle.

Mensuration

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