Can You Find The Shaded Area?

Added: 2026-06-02

[00:00:00]Given two semi circle inside a bigger semi circle.

[00:00:08]And AB is X.

[00:00:12]BC is 4X.

[00:00:16]And perimeter is 10 pi.

[00:00:22]And we have to find shaded area.

[00:00:27]So in any circle perimeter is 2 pi times radius.

[00:00:46]So in a semi circle the perimeter it will be pi times radius.

[00:01:07]And AB is X.

[00:01:09]That means radius of this semi circle will be X divided by 2.

[00:01:19]That means perimeter it will be pi times X divided by 2.

[00:01:29]And BC is 4X.

[00:01:33]That means perimeter of this semi circle it will be pi times radius will be 2X.

[00:01:49]And radius of biggest semi circle It is SC divided by two.

[00:02:12]That will be 5 x divided by two.

[00:02:17]So, perimeter it will be pi times 5 x divided by two.

[00:02:29]And given perimeter is 10 pi.

[00:02:49]Given perimeter is 10 pi.

[00:02:58]That means pi times x over two plus pi times 2 x plus pi times 5 x over two is 10 pi.

[00:03:15]And we can take pi common.

[00:03:20]And it is x plus 4 x plus 5 x divided by two is 10 pi.

[00:03:34]And pi will get cancelled.

[00:03:39]And it is 10 x divided by two is 10.

[00:03:47]That means x is two.

[00:03:53]We get X is 2.

[00:04:01]And now radius of this semicircle is X divided by 2.

[00:04:27]That will be 2 divided by 2.

[00:04:31]And it is 1.

[00:04:34]Radius of this semicircle is 2X.

[00:04:40]That will be 2 * 2. And it is 4.

[00:04:46]And radius of this semicircle is 5X divided by 2.

[00:04:55]That will be 5 * 2 divided by 2. And it is 5.

[00:05:03]So shaded area it will be area of biggest semicircle minus area of the two smaller semicircles.

[00:05:24]That will be pi times radius is 5 a squared divided by 2 minus pi times 1 a squared divided by 2 minus pi times 4 a squared divided by two and it is 25 pi divided by two minus pi divided by two minus 16 pi divided by two and it is 25 pi divided by two minus 17 pi divided by two that will be 8 pi divided by two and it is 4 pi.

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