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Question

ABCD is a parallelogram with sides AB = 12 cm BC = 10 cm and diagonal AC = 16 cm The area of the parallelogram and the distance between the shorter sides are respectively

A
120.5 cm2 ; 12.05 cm
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B
119.8 cm2 ; 11.98 cm
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C
118.71 cm2 ; 11.87 cm
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D
117.9 cm2 ; 11.79 cm
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Solution

The correct option is B 119.8 cm2 ; 11.98 cm
Area of Parallelogram ABCD=2×arABC
arABC=s(sa)(sb)(sc)
s=a+b+c2=16+10+122=19cm
arABC=19(1916)×(1910)(1912)
=169×3×9×7
=59.9cm2
area of parallelogram ABCD=2×59.9=119.8cm2
Now, area of parallelogram ABCD=base X height
119.8=10×hh=11.98cm
Distance between the shortest sides is 11.98cm

924400_271598_ans_e85b37a19da244e584e92b4f94ddbbcb.png

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