AC and BD are diagonals of the rhombus ABCD with side = 20 cm One diagonal of a rhombus is half the other, let AC = $$4x$$ cm => BD = $$2x$$ cm Diagonal of a rhombus perpendicularly bisect each other. => OD = $$x$$ cm and OC = $$2x$$ cm In $$ riangle$$ OCD, => $$(OC)^2 + (OD)^2 = (CD)^2$$ => $$(2x)^2 + (x)^2 = (20)^2$$ => $$4x^2 + x^2 = 400$$ => $$x^2 = frac{400}{5} = 80$$ $$ herefore$$ Area of rhombus = $$frac{1}{2} imes$$ Product of diagonals = $$frac{1}{2} imes 4x imes 2x$$ = $$4x^2 = 4 imes 80 = 320 cm^2$$ => Ans - (A)