Question

In the following figure, ABCD is a rectangle with AB = 14 cm and BC = 7 cm. Taking DC, BC and AD as diameters, three semi-circles are drawn as shown in the figure. Find the area of the shaded region.​

Answer 1

Answer:

The Area of shaded region is 59.5 cm².

Step-by-step explanation:

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  

AREA OF SEMICIRCLE with DIAMETER DC = 77 cm²

AREA OF RECTANGLE (ABCD) = Length × Breadth

= AB × DC  

= 14 × 7  

AREA OF RECTANGLE (ABCD) = 98 cm²

AREA OF 2 SEMI CIRCLE with DIAMETER BC & AD = 2 × 1/2πr²  

= (22/7) × (7/2)²  

= 11 ×7 / 2

AREA OF 2 SEMI CIRCLE with DIAMETER BC & AD  = 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.

HOPE THIS ANSWER WILL HELP YOU….

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