Question

How do you solve this problem?

Answer 1

The arcs $AB, BC, AC$ all equal to the third of the perimeter since equilateral triangle divides them like this.

So we need to find a perimeter but we are only given the area.

Let's review,

$

A=\pi r^2 \\

P=2\pi r

$

That means that from area we area able to calculate radius.

$A=\pi r^2\Longrightarrow r=\sqrt{\dfrac{A}{\pi}}$

Insert the numbers,

$r=\sqrt{\dfrac{36\pi}{\pi}}=6$

Then use the perimeter formula to calculate perimeter since radius is known,

$P=2\pi\cdot6=12\pi$

Now divide perimeter by 3 to get length of AB arc.

$AB=\dfrac{12\pi}{3}=\boxed{4\pi}$

Hope this helps.