Question 53
The perimeter of an equilateral triangle is 36 cm. What is the area of this triangle?
Solution
The perimeter of an equilateral triangle is 36 cm.
the perimeter of an equilateral triangle = $$3\times length\ of\ each\ side\ =36\ $$
$$length\ of\ each\ side=12$$
Area of this triangle = $$\frac{\sqrt{\ 3}}{4}\times\left(length\ of\ each\ side\right)^2$$
= $$\frac{\sqrt{\ 3}}{4}\times\left(12\right)^2$$
= $$\frac{\sqrt{\ 3}}{4}\times144$$= $$\sqrt{\ 3}\times36$$
= $$36\sqrt{\ 3}$$ cm$$^2$$
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