Hi, I am stuck with this example from prep swift

Two parts which I am stuck

Part 1

Why do we cut the triangle at such an odd shape (in ref to the 30-60-90 triangle). Why can’t we cut the equilateral such that the height of the 30-60-90 triangle is equal to the radius 6 and find the length of hypotenuse? Then, multiplies twice to get the full length of the side which then allow us to use “ice ice baby” to calculate the equilateral triangle area? I tried this but my answer is not the same at all

Part 2

If we follow the method from the video, length of the side of the equilateral triangle should be (3)(root 3) x 2 = 9 (root 3). Then we use ice ice baby where [(9) (root 3) ] / 2 multiples with [(9) (root 3) ] / 2 multiples with (root 3) = 60.75 (root 3) which is obviously different than Greg’s answer. Where have I gotten it wrong?

Thank you in advance.

Thought someone had responded, apologies.

So that we can divide the circle into triangles that are 30-60-90 (or another type covered on the GRE). To be clear, this is not the only option possible - another option is to divide the triangle into three congruent interior triangles - but then you’ll need to use the sine rule which is not on the GRE.

Sketch a diagram.

Spot your mistake there.

I figured it out and I think I got the concept right but somehow my answer is not right. Can I trouble your help again?

I found out that the length of the hypotenuse of 30-60-90 angle is 3.(square root 3), which we x2 to get the full length of one side of equilateral triangle which is = 27

To find the area of equilateral triangle, I use Ice x ice x baby = (27/2 x 27/2 x square root 3) = 315.7 but again, the answer differs from 27.(square root 3) = 46.8.

Where have I gotten it wrong this time?

(3 \sqrt{3})^2 = 27, which I don’t think is what you intended to do?

Hi thank you for replying. Really thankful for your help. But I do not get your question (Don’t intend to introduce the hammer ) Shouldn’t we multiple it by two to get the full length of one side so that we can plug it in for the ice-ice-baby equation to find the area of equilateral triangle?

You’re squaring, not multiplying by two.