Question

in fig abcd is a rectangle of side 14x7 find the area of shaded portion​

Answer 1

$\huge\colorbox{pink}{Question࿐ }$

In fig. ABCD is a rectangle with AB= 14 cm and BC= 7 cm. Taking DC, BCand AD as diameter, three semicircles are drawn. Find the area of the shaded portion.

$\huge\mathfrak\red{Solution:-}$

Given:

Length of a rectangle (AB) = DC = 14 cm

Breadth of a rectangle( BC) = AD=7 cm

→ AREA OF SEMICIRCLE with DIAMETER DC= 1/2πr² = ½(22/7) × (14/2)²

= 11 × 7 = 77 cm²

→ AREA OF RECTANGLE (ABCD) = Length × Breadth = AB × DC = 14 × 7 = 98 cm²

→ AREA OF 2 SEMI CIRCLE with DIAMETER BC & AD= 2× 1/2πr² =(22/7) × (7/2)² = 11 ×7 / 2

= 77 /2 cm²

→ AREA OF SHADED REGION = Area of rectangle ABCD - area of semicircle with diameter DC + Area of 2 semicircle with diameter BC and AD

→ Area of shaded region = 98 - 77 + 77/2

= 21 + 77/2 = (42 +77)/2 = 119/2 = 59.5 cm²

→ Area of shaded region = 59.5 cm²

Hence, the Area of shaded region is 59.5 cm².

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