The formula for the area of a circle is \(\displaystyle \dpi{100} \pi r^{2}\)

\(\displaystyle \dpi{100} \pi r^{2}= \pi (10)^{2}=100\pi\)

To find the area of a circle you must plug the radius into \(\displaystyle r\) in the following equation \(\displaystyle A=\pi(r^{2})\)

In this case the radius is 7 so we plug it into \(\displaystyle r\) to get \(\displaystyle 7^{2}=49\)

We then multiply it by pi to get our answer \(\displaystyle A=49\pi\)

To solve this question you must know the formula for the area of a rectangle.

The formula is \(\displaystyle A=B*H\)

In this case the rectangle is a square so we can plug in the side length for both base and height to yield \(\displaystyle A=8*8\)

Perform the multiplication to arrive at the answer of \(\displaystyle A=64\)

Let \(\displaystyle r\) be the radius of the circle. The area of the circle is 

\(\displaystyle A_{1} = \pi r^{2}\)

\(\displaystyle r\) is also the sidelength of the equilateral triangle. The area of the triangle is 

\(\displaystyle A_{2} = \frac{\sqrt{3}}{4} \; r^{2}\)

The percent of the circle covered by the triangle is:

\(\displaystyle \frac{A_{2} }{A_{1}} \cdot 100= \frac{\frac{\sqrt{3}}{4}r^{2}}{\pi r^{2}}\cdot 100 = \frac{100 \sqrt{3}}{4 \pi } \approx 14\)

The area of Julie's lawn is \(\displaystyle 265 \cdot215 = 56,975\) square feet. The amount of grass seed she needs is \(\displaystyle 56,975 \div 400 \approx 142.4\) pounds. This requires three fifty-pound bags, the most economical option since it is cheaper to buy a fifty-pound bag for $66 than five ten-pound bags for $100.00. Julie will spend \(\displaystyle \$66 \cdot3 = \$198\)

To make this easier, we will assume that the rectangle has length 5 and the square has sidelength 3. Then the area of the entire figure is 

\(\displaystyle (3 + 5) \times 3 = 24\),

and the area of the square is 

\(\displaystyle 3 \times 3 = 9\)

The square, therefore, takes up

\(\displaystyle \frac{9}{24} \times 100 = \frac{900}{24} = 37.5 \%\)

of the entire figure.

The large rectangle has length 80 and width 40, and, consequently, area

\(\displaystyle 80 \times 40 = 3,200\).

The white region is a rectangle with length 30 and width 20, and, consequently, area 

\(\displaystyle 30 \times 20 = 600\).

The white region is 

\(\displaystyle \frac{600}{3,200} \times 100 = 18 \frac{3}{4} \%\)

of the large rectangle.

Each side can be divided into three 3-foot sections.  This gives a total of \(\displaystyle 3\times3=9\) squares.  Another way of looking at the problem is that the total area of the large square is 81 and each smaller square has an area of 9.  Dividing 81 by 9 gives the correct answer.

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. 

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.