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Question : The two adjacent sides of a parallelogram are 12 cm and 5 cm respectively. If one of the diagonals is 13 cm long, then what is the area of the parallelogram?

Option 1: 60 cm2

Option 2: 30 cm2

Option 3: 75 cm2

Option 4: 25 cm2


Team Careers360 16th Jan, 2024
Answer (1)
Team Careers360 22nd Jan, 2024

Correct Answer: 60 cm 2


Solution :
In $\triangle$ABC, AB = 12 cm, BC = 5 cm and AC = 13 cm
The semiperimeter ($s$) = $\frac{12+5+13}{2}$ = 15 cm
So, the area of $\triangle$ABC
= $\sqrt{15(15-13)(15-12)(15-5)}$
= $\sqrt{15×2×3×10}$
= 30 cm 2
Now, the area of the parallelogram ABCD = 2 × the area of $\triangle$ABC = 2 × 30 = 60 cm 2
Hence, the correct answer is 60 cm 2 .

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