• # question_answer The height of a triangle is equal to the perimeter of a square whose diagonal is $6\sqrt{2}m$ and the base of the same triangle is equal to the side of a square whose area is$324\,\,{{m}^{2}}$. What is the area of the triangle? A) $215\,\,{{m}^{2}}$                 B) $216\,\,{{m}^{2}}$     C)        $220\,\,{{m}^{2}}$     D)        $195\,\,{{m}^{2}}$ E) $223\,\,{{m}^{2}}$

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$\text{=}\frac{\text{1}}{\text{2}}\text{ }\!\!\times\!\!\text{ Base }\!\!\times\!\!\text{ Height}$ $=\frac{1}{2}\times 18\times 24=216\,\,{{m}^{2}}$