Question

The adjacent sides of a parallelogram are 51 cm and 37 cm and it's diagonal is 20 cm . Find the area of the parallelogram ?

Answer 1

Answer: 612 cm²

Step-by-step explanation:

Use herons formula and multiply by 2

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Assumption

PQRS is parallelogram

Diagonal = 20 cm (QS)

$\textbf{\underline{Two\;adjacent\;sides:-}}$

PQ = 51 cm

PS = 37 cm

Now,

PS = 37 cm

PS = b = 37 cm

QS = c = 20 cm

Hence,

$\tt{\rightarrow s=\dfrac{a+b+c}{2}}$

$\tt{\rightarrow s=\dfrac{51+37+20}{2}}$

$\tt{\rightarrow s=\dfrac{108}{2}}$

s = 54 cm

Therefore

${\boxed{\sf\:{Area\;of\;parallelogram=2\times area\;of\; \triangle PQS}}}$

$\tt{\rightarrow 2\times\sqrt{s(s-a)(s-b)(s-c)}}$

$\tt{\rightarrow 2\times\sqrt{54(54-51)(54-37)(54-20)}}$

$\tt{\rightarrow 2\times\sqrt{54\times 3\times 17\times 34}}$

$\tt{\rightarrow 2\times\sqrt{9\times 3\times 2\times 3\times 17\times 2\times 17}}$

$\tt{\rightarrow 2\times\sqrt{3^2\times 3^2\times 2^2\times 17^2}}$

= 2 × 3 × 3 × 2 × 17 cm²

= 36 × 17 cm²

= 612 cm²