Question

The lengths of two adjacent sides of a parallelogram are 5 cm and 3.5 cm respectively. One of its diagonals is 6.5 cm long, the area of the parallelogram is

• A. 8√3 sq.cm
• B. 12√3 sq.cm
• C. 15 sq. cm
• D. 10√3sq.cm

Answer 1

Answer:

D. 10√3sq.cm

Let consider ABCD is a parallelogram.

Given,

AB = 5 and BC = 3.5 and AC = 6.5

Area of ∆ABC:

s = $\frac{(5 + 3.5 + 6.5)}{2}=7.5$

Area =$\sqrt{(7.5\times{(7.5-5)}\times{(7.5-3.5)}\times{(7.5-6.5)}}$

$=\sqrt{(7.5\times{2.5}\times{4}\times{1}}$

$=5\sqrt{3}$

Area of parallelogram $=2\times{5\sqrt{3}}=10\sqrt{3}$ sq. cm