If the length of a diagonal of a square is (a +b), then the area of the square is :
Answer & explanation
Correct answer: option 2
We know that,
Diagonal of a square = \(\sqrt {2}\) Side
Area of a square = (Side)2
We havem,
The length of a diagonal of a square = (a + b)
Side of the square = \(\frac{ Diagonal of a square }{\sqrt {2}}\)
⇒ Side of the square = \(\frac{ (a + b)}{\sqrt {2}}\)
The area of the square = [\(\frac{ (a + b)}{\sqrt {2}}\) ]2
= \(\frac{ (a + b)^2}{2}\)
=\(\frac{ ((a^2 + b^2 + 2ab))}{2}\) = \(\frac{ ((a^2 + b^2))}{2}\) + ab