Question

The length of two adjacent sides of a parallelogram are 5 cm and 3.5cm. One of its diagonals is 6.5cm long. Area of the parallelogram is

• A. $13\sqrt{10}c{m}^2$
• B. $23\sqrt{5}c{m}^2$
• C. $10\sqrt{5}c{m}^2$
• D. $10\sqrt{3}c{m}^2$

Answer 1

The correct option is D $10\sqrt{3}c{m}^2$

Area of the parallelogram ABCD
$=2\times \left(Areaof\Delta ABC\right)$
In $\Delta ABC$, AB = 5cm, BC = 3.5 cm and AC = 6.5 cm.
So its perimeter $s=\frac{5+3.5+6.5}{2}=7.5cm$
$\because$ Area of $\Delta ABC$ (By Heron’s formula)
$=\sqrt{s(s-a)(s-b)(s-c)}$
$=\sqrt{7.5\times (7.5-5)\times (7.5-3.5)\times (7.5-6.5)}sq.cm$
$=\sqrt{7.5\times 2.5\times 4\times 1}sq.cm=\sqrt{75}sq.cm$
$=5\sqrt{3}sq.cm$
$=2\times 5\sqrt{3}sq.cm$
Area of parallelogram
$=2\times 5\sqrt{3}sq.cm=10\sqrt{3}sq.cm$