Question : The perimeter of an equilateral triangle is 48 cm. Find its area (in cm2).
Option 1: $81\sqrt{3}$
Option 2: $8\sqrt{3}$
Option 3: $25\sqrt{3}$
Option 4: $64\sqrt{3}$
Correct Answer: $64\sqrt{3}$
Solution :
Let $a$ be the side of an equilateral triangle.
The perimeter of an equilateral triangle = 48 cm
So, $3a= 48$
$\therefore a= 16$
Now, the area of an equilateral triangle
= $\frac{\sqrt3a^2}{4}$
= $\frac{\sqrt3×16^2}{4}$
= $64\sqrt3$ cm
2
Hence, the correct answer is $64\sqrt3$.
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