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
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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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