Can you find the area of the square?

[00:00:00]Can you find the area of the square ABCD given ABCD is a a square.

[00:00:21]That means these angles they will be 90° and if AB is X then BC will be X.

[00:00:38]AD will be X.

[00:00:46]And suppose AP is A then DP is AD minus AP and AD is X minus AP is A.

[00:01:08]DP is X minus A.

[00:01:14]And suppose this angle is alpha then this angle will be 90° minus alpha and this angle is 90° that means this angle it will be again alpha.

[00:01:44]And now in triangle BAP and triangle PDQ angle BAP is equal to angle PDQ that is 90° and angle ABP is equal to angle DPQ that is alpha so triangle BAP it will be similar to triangle PDQ hence BA over PD it will be BP over PQ and BA is X over PD is X minus A and BP is three over PQ is two and if we cross multiply then two times X it will be three times x minus a and 2x it's 3x minus 3a So, 3a It will be 3x minus 2x and 3a is x.

[00:04:15]We get x is 3a.

[00:04:21]And Now in triangle BAP BA squared plus AP squared it will be BP squared.

[00:04:53]And BA is x that is 3a.

[00:05:01]a squared plus AP is a a squared and BP is 3a squared.

[00:05:11]And 9a squared plus a squared is nine.

[00:05:17]And 10a squared is nine.

[00:05:21]So, a squared it is nine divided by 10.

[00:05:32]And Now area of ABCD it will be side S squared.

[00:05:53]And side is X.

[00:05:56]That is 3A.

[00:05:59]S squared And it is 9 A squared.

[00:06:04]That will be 9 times and A is squared is 9 over 10.

[00:06:13]That will be 81 over 10.

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