+110 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.
+128473 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
