What will be the perimeter of an equilateral triangle inscribed in a circle of area154 sq.cm?

Answer 1

The formula for area of a circle is Area=pi*radius2

you know the area of your circle so now find the radius.

154 = pi*r2

r = 7 cm

if you can imagine the equilateral triangle in the circle imagine that the radius touches the exact center of this triangle and can extend to one of the three points on the triangle. (this next part would be so much easier if i could draw you a picture). now, if you remember that an equilateral triangle has three angles that each measure up to 60 degrees. if you take the radius of the circle and draw a line from the center of the triangle to the tip of the triangle you will actually cut on of the 60 degree angles in half. this would now make you have an angle 30 degrees. if you do this same thing to another point you will notice you actually have another triangle inside this triangle. since all triangle angles add up to 180 degrees you know all three angles of this new triangle. (note: this new triangle is not an equilateral triangle). so this new triangle has an angle 30 degrees, 30 degrees, and 120 degrees. you can now use the law of sines to find out the length of one side of the equilateral triangle. if you have drawn your picture correctly then you will see that one side of the new triangle actually shares one side of the equilateral triangle. if you look at your new triangle their is only one side that is known a known quantity. this side is the side that is shared with the equilateral triangle. use the law of sines to figure out the length of this side...

7 / sin(30) = x / sin(120)

x = 12.12cm

you now know that one side of the equlateral triangle is 12.12cm. since there is three sides to the triangle the total perimeter of the equilateral triange is 12.12 times 3

your answer for the perimeter of the equilateral triangle is 36.36cm