Hello, svetka!

Another approach . . .

A circle is inscribed in an equilateral triangle of side 8.

Find the area of the circle. Code:

*
/ \
/ \
/ \
/ \
/ \
/ * * * \
/* *\
* *
* \ / *
/ r\ /r \
/* \ / *\
/ * * * \
/ * | * \
/ | \
/ * |r * \
/ * | * \
/ * | * \
*-------------*-*-*-----------------*
: - - - - - - - - 8 - - - - - - - - :

The area of an equilateral triangle of side is: .

We have , so: .

Formula: .The area of a triangle is: .

. . . . . . . where is the perimeter, and is the radius of the inscribed circle.

The perimeter of this triangle is 24, so we have: .

Hence: .

Now you can find the area of the circle . . .