Question

# If the diagonal of a square is 8 cm, then its area is(a) $4c{{m}^{2}}$ (b) $16c{{m}^{2}}$(c) $24c{{m}^{2}}$(d) $32c{{m}^{2}}$

Hint: Use the property that area of the square is equal to half of the square of the length of the diagonal of the square, i.e., area of the square is $\dfrac{{{l}^{2}}}{2}$ , where l is the length of the diagonal. So, just put the length of the diagonal in the formula and solve to get the answer.

$\therefore \text{ Area of the square = }\dfrac{{{\left( diagonal \right)}^{2}}}{2}$
$\text{Area of the square = }\dfrac{{{8}^{2}}}{2}$
$\text{Area of the square = }\dfrac{64}{2}=32c{{m}^{2}}$
Note: We could have also solved the above question using the property that the diagonal of a square is $\sqrt{2}$ times the length of its side followed by the use of the formula that the area of the square is equal to the square of the length of its side.