The area of a circle inscribed in a regular triangle is 16п cm2. Find the area of the circle described around this triangle.

Let us determine what the radius of the circle that is inscribed in this triangle will equal, if from the condition of the problem we know for sure that its area is 16π cm2:

√ (16π: π) = √16 = 4.

Let us determine what the side of this regular triangle will equal, because we know that the radius of such a circle is calculated by the formula a / 2√3:

4 * 2√3 = 8√3.

Let’s determine what the radius of the circle described around it will equal:

8√3: √3 = 8.

Let’s determine what the area of this circle will be:

π * 8 ^ 2 = 64π.

Answer: Area = 64π.