Two adjacent sides of a parallelogram are 21 cms and 20 cms. The diagonal joining the end points of these two sides is 29 cms. The area of the parallelogram (in sq.cms) is

A diagonal divides the parallelogram into two triangles of equal areas.

Sides of triangle, $$a=29$$ cm , $$b=21$$ cm and $$c=20$$ cm

Semi-perimeter, $$s=\frac{a+b+c}{2}=\frac{29+21+20}{2}$$

=> $$s=\frac{70}{2}=35$$ cm

Area of triangle using Heron's Formula = $$\sqrt{s(s-a)(s-b(s-c)}$$

= $$\sqrt{35(35-29)(35-21)(35-20)}$$

= $$\sqrt{35 \times 6 \times 14 \times 15}$$

= $$\sqrt{44100}= 210$$ $$cm^2$$

=> Area of parallelogram = $$2 \times 210=420$$ $$cm^2$$

=> Ans - (D)