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

Question

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 · Accepted Answer

Correct Answer: 60 cm²

Solution :
In $ riangle$ABC, AB = 12 cm, BC = 5 cm and AC = 13 cm
The semiperimeter ($s$) = $\frac{12+5+13}{2}$ = 15 cm
So, the area of $ riangle$ABC
= $\sqrt{15(15-13)(15-12)(15-5)}$
= $\sqrt{15×2×3×10}$
= 30 cm²
Now, the area of the parallelogram ABCD = 2 × the area of $ riangle$ABC = 2 × 30 = 60 cm²
Hence, the correct answer is 60 cm².

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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 cm2Option 2: 30 cm2Option 3: 75 cm2Option 4: 25 cm2

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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