Let the side of square = $$s$$ cm and diagonal, $$d=9$$ cm => $$(s)^2+(s)^2=(d)^2$$ => $$2s^2=9^2=81$$ => $$s^2=frac{81}{2}$$ => $$s=sqrt{frac{81}{2}} = frac{9}{sqrt{2}}$$ Thus, perimeter of square = $$4s$$ = $$4 imes frac{9}{sqrt{2}} = 18sqrt{2}$$ cm Also, perimeter of square = Perimeter of equilateral triangle = $$18sqrt{2}$$ cm Let side of equilateral triangle = $$a$$ cm => $$3a=18sqrt{2}$$ => $$a=frac{18sqrt{2}}{3} = 6sqrt{2}$$ cm $$ herefore$$ Area of equilateral triangle = $$frac{sqrt{3}}{4} a^2$$ = $$frac{sqrt{3}}{4} imes (6sqrt{2})^2$$ = $$18sqrt{3}$$ $$cm^2$$ => Ans - (A)