Question

can someone please help me

Answer 1

Find the Area of the circle if every vertices of the equilateral triangle is on the circumference of the circle.

Answer 2

You have a 60, 60, 60 triangle based on your sides.

Answer 3

any ideas?

Answer 4

Okay what you need to do is calculate the three sectors created here. you can see that all angles in that triangle are equal and as they are all equal they all equal 180/3 = 60 degrees.

Now the area of a sector is given by

Area of Sector = x/360 * Pi * r^2 where x is the angle of the sector.

So one of the three sectors created by the above triangle = 1/6 * Pi * 2^2

Once you calculate that you simply multiply the answer by three to get the area of all three sectors and you will have the area of the circle.

Answer 5

doesn't it will have 3 area of the triangle

Answer 6

Okay. What you need here is the radius of the circle. That is the distance from the center of the circle to any point on the circle, and happily any vertex of the triangle is a point on the circle. Also, I won't prove it, but I hope you grant that the center of the triangle is the center of the circle.

How do you find the center of the triangle?