Question

Two adjacent sides of a parallelogram are $34$ cm and $20$cm. One of its diagonals is $42$ cm. Then the area of the parallelogram is

• A. $612$ sq.cm
• B. $672$ sq.cm
• C. $784$ sq.cm
• D. $796$ sq.cm

Answer 1

The correct option is B $672$ sq.cm

REF.image

Area of triangle = $\sqrt{S(S-a)(S-b)(S-c)}$

( Here, S is the semi-perimeter)

$S=\frac{a+b+c}{2}$

$\Rightarrow S=\frac{42+20+34}{2}$

$\Rightarrow S=\frac{96}{2}$

$\Rightarrow S=48cm$

Area of $\Delta ABC=\sqrt{48(48-34)(48-20)(48-42)}$

$=\sqrt{48\times 14\times 28\times 6}$

$=336c{m}^2$

Now,

Area of parallelogram = $2\times$ Area of $\Delta ABC$

$=2\times 336$

$=627c{m}^2$

$\therefore$ so, the answer is B. $672c{m}^2$ or $672$ sq.cm