Question : A parallelogram has sides 15 cm and 7 cm long. The length of one of the diagonals is 20 cm. The area of the parallelogram is:
Option 1: 42 cm2
Option 2: 60 cm2
Option 3: 84 cm2
Option 4: 96 cm2
Correct Answer: 84 cm 2
Solution :
Given: A parallelogram has sides 15 cm and 7 cm long. The length of one of the diagonals is 20 cm.
Let ABCD be the parallelogram.
The diagonal of a parallelogram divides it into two equal triangles.
The half perimeter of one of the triangles, $s$ = $\frac{15+7+20}{2}=21$ cm
Area of triangle by heron's formula = $\sqrt{s(s-a)(s-b)(s-c)}$
So, the area of one of the triangles is:
= $\sqrt{21(21-15)(21-7)(21-20)}$
= $\sqrt{21×6×14×1}$
= 42 cm
2
So, Area of the parallelogram = 2 × Area of one of its triangles = (2 × 42) cm
2
= 84 cm
2
Hence, the correct answer is 84 cm
2
.
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