Question

If the length of the diagonal of a square is 5$\sqrt{2}$ ,then find its area

• A. 25 $c{m}^2$
• B. 10 $c{m}^2$
• C. 25 $\sqrt{2}$ $c{m}^2$
• D. 10$\sqrt{2}$ $c{m}^2$

Answer 1

The correct option is A 25 $c{m}^2$

Square is also a rhombus whose diagonals are equal
Hence area of square = area of rhombus

= $\frac{1}{2}$$\times$(product of diagonals)
Area of square = area of rhombus = $\frac{1}{2}$ $\times$ (diagonal)${}^2$ [ since diagonals are equal]

Area of square = area of rhombus = $\frac{1}{2}$$\times$$5\sqrt{2}$$\times$$5\sqrt{2}$

​Area of square = area of rhombus = 25$c{m}^2$