A) \[48\text{ }c{{m}^{2}}\]
B) \[96\,\,c{{m}^{2}}\]
C) \[144\text{ }c{{m}^{2}}\]
D) \[192\text{ }c{{m}^{2}}\]
Correct Answer: B
Solution :
| [b] Side of a rhombus \[(a)=10\,\,cm\] and diagonal \[{{(d)}_{1}}=12\,cm\] We know that \[4{{a}^{2}}={{d}^{2}}+d_{2}^{2}\] \[\Rightarrow \] \[4\times {{(10)}^{2}}={{(12)}^{2}}+d_{2}^{2}\] \[\Rightarrow \] \[4\times 100=144+d_{2}^{2}\] \[\Rightarrow \] \[d_{2}^{2}=100=144+d_{2}^{2}\] \[\Rightarrow \] \[{{d}_{2}}=16\,cm\] Now, area of rhombus \[=\frac{1}{2}\times {{d}_{1}}\times {{d}_{2}}=\frac{1}{2}\times 12\times 16=6\times 16=96\,c{{m}^{2}}\] |
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