A parallelogram has sides 60 m and 40 m and one of its diagonals is 80 m long. Its area is
A. $$500\sqrt {15} {\text{ }}{{\text{m}}^2}$$
B. $$600\sqrt {15} {\text{ }}{{\text{m}}^2}$$
C. $$400\sqrt {15} {\text{ }}{{\text{m}}^2}$$
D. $$450\sqrt {15} {\text{ }}{{\text{m}}^2}$$
Answer: Option B
Solution (By Examveda Team)
$$\eqalign{ & S\left( {\Delta ABD} \right) = \frac{{60 + 80 + 40}}{2} = 90 \cr & {\text{ar }}\Delta ABD = \sqrt {90\left( {90 - 80} \right)\left( {90 - 60} \right)\left( {90 - 40} \right)} \cr & = \sqrt {90 \times 10 \times 30 \times 50} \cr & = 300\sqrt {15} {\text{ }}{{\text{m}}^2} \cr & {\text{ar }}\square ABCD = 2 \times {\text{ar }}\Delta ABD = 600\sqrt {15} {\text{ }}{{\text{m}}^2} \cr} $$
This Question Belongs to Arithmetic Ability >> Mensuration 2D
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