A) \[\frac{15}{4}c{{m}^{2}}\]
B) \[\frac{15}{4}\sqrt{7}c{{m}^{2}}\]
C) \[\frac{4}{15}\sqrt{7}c{{m}^{2}}\]
D) None of these
Correct Answer: B
Solution :
We have, \[a=4cm\], \[b=5cm\],\[c=6cm\] Semi-perimeter (s) = \[\frac{a+b+c}{2}\]= \[\frac{4+5+6}{2}=\frac{15}{2}\] cm Area of triangle = \[\sqrt{s\,(s-a)\,(s-b)\,(s-c)}\] = \[\sqrt{\frac{15}{2}\,\left( \frac{15}{2}-4 \right)\,\left( \frac{15}{2}-5 \right)\,\left( \frac{15}{2}-6 \right)}\,\]= \[\frac{15}{4}\sqrt{7}c{{m}^{2}}\].
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