Question
Thu February 26, 2009 By: Manpreet Dhillon

Respected sir, I was not able to solve the following question. Please solve it for me. Please get the answer because i couldnt get the answer.

Find the area of shaded region:

Find area

Expert Reply
Sat February 28, 2009

Name the point of the full sector where the angle is 90 degrees as O(say)

Name the point where the two semicircles meet as A.

Name the  end point on the vertical line  segment as B and on the horizontal line  segment as C.

From A drop perpendiculars to both semicircles meeting them at M and N (say)

So AM=AN=3.5 cm (1/2 of the diameter)

Area of sector MOA=(90/360)*(22/7)*(3.5)*(3.5)

area triangle MOA=1/2*(3.5)*(3.5)

Subtract the area of the triangle from the area of the sector you wil get the area of half the shaded portion(for the simicircles)=3.5Double that will be the area of the shaded portion common to the semicircles=3.5*2=7 sq cm area of the full big sector=(90/360)(22/7)(7)(7)=77/2=38.5 sq cm

From this if we subtract the area of both the semicircles , we will get the area of the top shaded portion.

now area of the two semicircles = area of both semicircles- area of the common part , the shaded portion.(we need to subtract this as it gets counted twice in the area of the semicircles)

[(22/7)*3.5*3.5)] -7=38.5-7=31.5sq cm

So area of the top shaded part=area of full sector-area of two semi circles=38.5-31.5=7

So area of the total shaded part

=area of top shaded part+area of lower shaded part

=7+7=14 sq cm

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