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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. - Mathematics

Sum

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

 

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Solution

Area of the shaded region can be calculated as shown below,

Area of the shaded region = Area of rectangle − area of the semi-circle with diameter DC triangle + 2 `xx`area of two semicircles with diameters AD and BC

`∴ "'Area of the shaded region"=7xx14-(pixx7^2)/2+2xx (pixx3.5^2)/2` 

`∴ "Area of the shaded region"=98-pixx49/2+pixx12.25` 

Substituting `pi=22/7` we get,

` ∴"Area of the shaded region"=7xx14-pixx7^2/2+2xx pixx3.5`

Substituting `pi=22/7 "We get"` 

`∴"Area of the shaded region"=98-(22/7xx49)/2+22/7+12.25`

`∴"Area of the shaded region"=98-(22xx7)/2+22xx1.75`

`∴"Area of the shaded region "98-77+22xx1.75`

`∴"Area of the shaded region "21+38.5`

`∴"Area of the shaded region "=59.5`

Therefore, area of the shaded region is `59.5 cm^2`

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 13 Areas Related to Circles
Exercise 13.4 | Q 15
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