Question

Find the area of a parallelogram ABCD in which AB = 3 cm and BC = 4 cm and AC = 5 cm using Heron's formula.

• A. 6 cm²
• B. 12 cm²
• C. 18 cm²
• D. 24 cm²

Answer 1

The correct option is B

12 cm²

Since ABCD is a parallelogram, its opposite sides will be equal.

AB = 3 cm, BC = 4 cm and AC = 5 cm

Now in triangle ABC,

Area of the triangle using heron’s formula,

$s=\frac{Perimeter}{2}=\frac{3+4+5}{2}=6cm$

Area = $\sqrt{s(s-a)(s-b)(s-c)}$
= $\sqrt{6(6-3)(6-4)(6-5)}$
= $\sqrt{36}$
= $6c{m}^2$

Area of the parallelogram = 2 (Area of triangle ABC)

$\Rightarrow \text{The area of the parallelogram}=2\times 6=12c{m}^2$