Can you find the shaded area?

Ajouté : 2026-05-12

[00:00:00]Can you find this shaded area in triangle ABC?

[00:00:21]It is A B C This angle is 60° This angle is 60° So, this angle it will be also 60° That means AB BC and AC they will be equal Suppose A and CQ is BC - BQ and BC is A BQ is 15 So, CQ is A - 15 and CP is CA AP and CA is A AP is 5 CP is A - 5 and this angle is 60° and >> Now, in triangle CPQ, cos 60° it will be base CQ over hypotenuse is CP.

[00:02:28]And cos 60° is 1 over 2.

[00:02:34]And CQ is A minus 15 over CP is A minus 5.

[00:02:44]And if we cross multiply, then A minus 5 it will be two times A minus 15.

[00:02:58]And A minus 5 is 2A minus 30.

[00:03:07]And minus 5 plus 30 it will be 2A minus A.

[00:03:21]So, 25 it is A.

[00:03:28]So, A is 25.

[00:03:33]And A minus 15 is 25 minus 15 that will be 10.

[00:03:43]And A minus 5 is 25 minus 5 that will be 20.

[00:03:55]And now in any triangle ABC if AB is A AC is B and this angle is theta then area of ABC is 1/2 times A times B times sin theta So area of CPQ it will be 1/2 times CQ times CP times sin 60° And it is 1/2 times CQ is 10 CP is 20 and sin 60° is root 3 over 2 And 2 * 5 is 10 2 * 10 is 20 So it is 5 times 10 times root 3 that will be 50 root 3 root three.

[00:05:55]>> [music]