Question

If the length of a diagonal of a square is a + b, then the area of the square is:

• A. $(a+b{)}^2$
• B. $\frac{1}{2}(a+b{)}^2$
• C. $a^2+b^2$
• D. $\frac{1}{2}(a^2+b^2)$

Answer 1

The correct option is B $\frac{1}{2}(a+b{)}^2$

A square is also a rhombus (all sides equal; also all angles, in case of square).

Area of rhombus is half the product of diagonals.

Hence here, area of square is $\frac{1}{2}\ast (a+b{)}^2$.