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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 10√3 cm2Given, 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(s−a)(s−b)(s−c)=√7.5(7.5−5)(7.5−3.5)(7.5−6.5)=5√3 cm2 ⇒ Area of parallelogram ABCD=2×area of triangle ABC=2×5√3 cm2=10√3 cm2

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