In the figure (i) given below, ABCD is a rectangle. AB = 14 cm, BC = 7 cm. From the rectangle, a quarter circle BFEC and a semicircle DGE are removed. Calculate the area of the remaining piece of the rectangle.
Mensuration
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Question

In the figure (i) given below, ABCD is a rectangle. AB = 14 cm, BC = 7 cm. From the rectangle, a quarter circle BFEC and a semicircle DGE are removed. Calculate the area of the remaining piece of the rectangle.

Mensuration

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KnowledgeBoat · Accepted Answer

Area of rectangle = AB × BC = 14 × 7 = 98 cm². Since, ABCD is a rectangle. ∴ CD = AB = 14 cm. BFEC is a quadrant of radius, BC = r₁ = 7 cm. ∴ CE = 7 cm. From figure, DE = CD - CE = 14 - 7 = 7 cm. From figure, DE is the diameter of semi-circle DGE. So, radius (r) = = 3.5 cm. Area of semi-circle = Area of quadrant BFEC = Area of remaining piece of rectangle = Area of rectangle - Area of semicircle DGE - Area of quadrant BFEC = 98 - 19.25 - 38.5 = 40.25 cm². Hence, area of remaining piece of rectangle = 40.25 cm².

Mathematics

In the figure (i) given below, ABCD is a rectangle. AB = 14 cm, BC = 7 cm. From the rectangle, a quarter circle BFEC and a semicircle DGE are removed. Calculate the area of the remaining piece of the rectangle.

Mensuration

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Mathematics

In the figure (i) given below, ABCD is a rectangle. AB = 14 cm, BC = 7 cm. From the rectangle, a quarter circle BFEC and a semicircle DGE are removed. Calculate the area of the remaining piece of the rectangle.

Mensuration

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