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Question

Two adjacent sides of a parallelogram are 5 cm and 3.5 cm. One of its diagonals is 6.5 cm. Then the area of parallelogram is

A
53 cm2
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B
103 cm2
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C
153 cm2
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D
203 cm2
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Solution

The correct option is C 103 cm2
Given, ABCD is a parallelogram having AB=5 cm,BC=3.5 cm and one of the diagonal AC=6.5 cm.
We know that the diagonal of a parallelogram divides it into two triangles of equal area.
Therefore, in triangle ABC, by heron's formula, we have a=5 cm,b=3.5 cm and c=6.5 cm
semi-perimeter of triangle ABC,s=a+b+c2=5+3.5+6.52=7.5 cm
Area of triangle ABC=s(sa)(sb)(sc)=7.5(7.55)(7.53.5)(7.56.5)=53 cm2
Area of parallelogram ABCD=2×area of triangle ABC=2×53 cm2=103 cm2

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