Question

2 adjacent sides of parallelogram are 5cm and 3.5cm .One of its diagonal is 6.5 CM. Find area of parallelogram

Answer 1

Let ||gm ABCD have sides AB=5cm, BC=3.5cm and diagonal AC = 6.5cm.

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

$= \frac{15}{2}$

$=7 .5$

$s - a = 7.5 - 5 = 2.5$

$s - b = 7.5 - 3.5 = 4$

$s - c = 7.5 - 6.5 = 1$

ar(ABC)

$= \sqrt{s(s - a)(s - b)(s - c)}$

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

$= 2 \sqrt{18.75} {cm}^{2}$

ar(ABCD)

$= 2 \times 2 \sqrt{18.75}$

$= 4 \sqrt{18.75} {cm}^{2}$

Therefore,

ar(ABCD)=4√18.75sq.cm

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