CRITICAL THINKING Find the area between the three congruent tangent circles. The radius of each circle is 6 inches. Round your answer to the nearest hundredth. Three congruent circles touch each other. The centers are marked as points A, B, and C. Equilateral triangle A B C is formed and the region inside triangle, but not in a circle, is shaded. The area is about a square inches.

Step-by-step explanation:

Given

--- The radius of each

Required

The area between them

See attachment for illustration of the question. (figure 1)

First, calculate the height of the equilateral triangle formed by the 3 radii (See figure 2)

Using Pythagoras theorem, we have:

Collect like terms

Take square roots

Expand

Split

Now, the area of the equilateral triangle can be calculated using:

Where

Next, is to calculate the area of the sector formed by 2 radii in each circle (figure 3).

Since the radii formed an equilateral triangle, then the central angle will be 60. So:

For the three circles, the area is:

Subtract the areas of the sectors (A2) from the area of the equilateral triangle (A1), to get the area between them.

Approximate

i'm pretty sure it's 477,585,296, but perhaps my math is incorrect.

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step-by-step explanation: