A) \[215\,\,{{m}^{2}}\]
B) \[216\,\,{{m}^{2}}\]
C) \[220\,\,{{m}^{2}}\]
D) \[195\,\,{{m}^{2}}\]
E) \[223\,\,{{m}^{2}}\]
Correct Answer: B
Solution :
Height of the triangle = Perimeter of the square = 4a \[\text{=4 }\!\!\times\!\!\text{ }\frac{\text{diagonal}}{\sqrt{\text{2}}}\text{=}\frac{\text{4 }\!\!\times\!\!\text{ 6}\sqrt{\text{2}}}{\sqrt{\text{2}}}\text{=24}\,\,\text{m}\] Base of the triangle\[=\sqrt{324}=18\,\,m\] \[\therefore \]Area of the triangle\[\text{=}\frac{\text{1}}{\text{2}}\text{ }\!\!\times\!\!\text{ Base }\!\!\times\!\!\text{ Height}\] \[=\frac{1}{2}\times 18\times 24=216\,\,{{m}^{2}}\]
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