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

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`