SOLUTION: A circle is inscribed in the equilateral triangle and its radius is 6 cm, what is the area of the equilateral triangle?

Algebra.Com
Question 1014588: A circle is inscribed in the equilateral triangle and its radius is 6 cm, what is the area of the equilateral triangle?
Answer by ikleyn(52908)   (Show Source): You can put this solution on YOUR website!
.
A circle is inscribed in the equilateral triangle and its radius is 6 cm, what is the area of the equilateral triangle?
--------------------------------------------------------------- 

Since the radius of the inscribed circle is r = 6 cm,
the side of the triangle is  = 20.785 cm.


Then the area of the triangle is the product of its semi-perimeter and the radius of the inscribed circle 

S =  =  = 187.06 .


See the lessons
 
  Formulas for area of a triangle 
  Proof of the formula for the area of a triangle via the radius of the inscribed circle

in this site.


RELATED QUESTIONS

A circle is inscribed in an equilateral triangle, the radius of the circle is 6 cm. Find... (answered by Fombitz)
An equilateral triangle is inscribed in a circle of a radius 6 cm., find its side (answered by josgarithmetic)
A circle is inscribed inside an equilateral triangle. If the circumference of the circle... (answered by Boreal)
Determine the area of an equilateral triangle inscribed in a circle of radius 12... (answered by Greenfinch)
what is the area of an equilateral triangle whose inscribed circle has radius... (answered by josgarithmetic)
An equilateral triangle is inscribed in a circle of radius 10cm , Find the area of... (answered by ikleyn)
an equilateral is inscribed in a circle of radius 10 cm. Find the equilateral's area. (answered by Alan3354)
An equilateral is inscribed in a circle of radius 10cm. Find the area of the equilateral. (answered by edjones)
An equilateral triangle is inscribed in a circle with a radius of 6". Find the area of... (answered by edjones)