Question

in the figure given below the two semi-circles are identical with diameter of 8cm. B and Dare the mid point if the ABC and CDE respectively. What is the area of the shaded

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Answer 1

Answer:

Hi,

the figure may look complicated but can be actually taken as one circle divided into two half..

We can work on one semicircle and then multiply the area of shaded region by 2..

join point B with th center of the diameter say, O..

so OBC is a right angle triangle, as B is the midpoint of arc AC...

what will be the area of shaded region..

=area of sector BC - area of triangle OBC..

sector BC is 1/4 of the circle of radius 2, so area = π *2^2/4= π ..

area of OBC= 1/2* (OB*OC)= 2^2/2=2..

so area of one shaded region= π - 2..

area of total shaded region= 2(π - 2)