A circle is inscribed inside an equilateral triangle. If the circumference of the circle is 6m then the area of the triangle in cm squared is.

Hans007
Oct 22, 2017

#1**+2 **

The radius of the circle is

6 = 2pi * r

r = 6 / [ 2 pi] = [ 3/pi] m

The center of the circle will lie on the angle bisectors....so

(1/2) the length of the base....call this "d"...... is given by

tan (30) = [ 3/pi] / d

1/√3 = 3 / [pi *d ] rearrange as

d = 3√3 / pi m

And the height of the triangle, h, is given by

tan (60) = h / d

√3 = h / [3√3 / pi]

√3 = pi * h /[ 3√3] rearrange as

9/pi m = h

So....the area of the triangle is :

(1/2)b * h =

d * h =

[3√3 / pi] m * 9/pi m =

[27√3] / pi^2 m ^2 ≈ 4.738 m^2 ≈ 4.738 * 100^2 cm^2 ≈ 47380 cm^2

CPhill
Oct 22, 2017