To find the area of a circle you must plug the radius into the following equation

In this case the radius is  so we plug it in and square it to get 

We then multiply it by  to get our answer 

Each set of two circles fits perfectly between the sides of the square. The diameters of two of the circle must equal the length of one side of the square.

Each side has a length of 8 and the diameter of a circle is twice the radius. We can use these relationships to substitute into the first equation.

Solve for the radius, .

The area of a circle can be calculated using the equation . The shaded region is made of four circles, all with the same radius.

The area of one circle is given below.

The area of the shaded region (four circles) would be .

The area of the shaded region can be found by using the areas of the individual circles. The area of the full figure is the area of circle O. The area of the center shaded area is the area of circle I. Circle M contains circle I. The area of the shaded region will be equal to .

First, find the area of each circle using .

Now we can substitute into our equation.

The formula for area of a circle is . Unfortunately, the problem gives us a diameter instead of a radius. The good news is that the diameter is equal to twice the length of the radius or, mathematically, . 

Plug in the given diameter to find the radius:

Plug that into our first equation to solve:

The area of the circle is  times radius squared ().

If the circumference is , then since  we know . We further know that , so 

The equation is already in a circle equation, and the right side of the equation stands for r^2 → r² = 81 and r = 9

The area of a circle is πr², so the area of this circle is 81π.

If you answered that the whirlpool’s area is 18.84 feet and therefore fits, you are incorrect because 18.84 is the circumference of the whirlpool, not the area.

If you answered that the area of the whirlpool is 56.52 feet, you multiplied the area of the whirlpool by 1.5 and assumed that that was the correct area, not the legal limit.

If you answered that the area of the backyard was smaller than the area of the whirlpool, you did not calculate area correctly.

And if you thought the area of the backyard was 30 feet, you found the perimeter of the backyard, not the area.

The correct answer is that the area of the whirlpool is 28.26 feet and, when multiplied by 1.5 = 42.39, which is smaller than the area of the backyard, which is 56 square feet. 

The total area of both circles is π + π = 2π

Since the region overlaps, we cannot count it twice, so we must subtract it.

we get 2π – π = π

Using the Pythagorean Theorem, the diameter of the circle (also the diagonal of the square) can be found to be 4√2.  Thus, the radius of the circle is half of the diameter, or 2√2.  The area of the circle is then π(2√2)², which equals 8π.  Next, the area of the square must be subtracted from the entire circle, yielding an area of 8π-16 square inches.