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Question

Two adjacent sides of a parallelogram are 10 cm and 12 cm. If one diagonal of it is 16 cm long; find area of the parallelogram. Also, find distance between its shorter sides.

A
119.8 cm2;11.98 cm
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B
119.9 cm2;11.20 cm
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C
117.6 cm2;10.28 cm
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D
120.8 cm2;15.98 cm
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Solution

The correct option is A 119.8 cm2;11.98 cm
Given, AB=12 cm, BC=10 cm
BD is the diagonal of parallelogram ABCD.
Also BD=16 cm
We know, ABDDCB [SSS Congruence]
Also, area of parallelogram ABCD = Area of ABD + Area of DCB
= 2 × Area of ABD
= 2s(s12)(s10)(s16)
s=12+10+162
= 19
Therefore, area of parallelogram ABCD= 219(1912)(1910)(1916)
= 23591
= 2(59.92)
= 119.8 cm2
Also, h is the distance of the two shorter sides.
We know, area of parallelogram = base×height
= BC×h
Therefore, h=Area of parallelogram ABCDBC
h=119.810
h=11.98 cm
306566_183019_ans.png

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