The area of a circle is found by: $\displaystyle Area=r^{2}\pi$, where r is the radius.

$\displaystyle 4^{2} \pi = 50.2$.

The area of the circle is $\displaystyle 50.2\ cm^{2}$.

The formula for the area, $\displaystyle A$, of a circle with radius $\displaystyle R$ is:

$\displaystyle A=\pi R^{2}$

We can fill in $\displaystyle R$

$\displaystyle A=\pi (18^{2})$

$\displaystyle A=324\pi$

You could do the arithmetic to get an area of about 1,017.876 square units, but it is ok and more precise to leave it as shown.

Half of the diameter 13 is the radius $\displaystyle \frac{13}{2}$. Use the area formula:

$\displaystyle A = \pi r^{2} = \pi \cdot \left ( \frac{13}{2} \right )^{2} = \frac{169\pi }{4}$

The area of a circle can be solved using the equation $\displaystyle A=\pi r^{2}$ 

The area of a circle with radius 4 is $\displaystyle \pi 4^{2}=16\pi$ while the area of a circle with radius 2 is $\displaystyle \pi 2^{2}=4\pi$. $\displaystyle 16\pi \div 4\pi =4$

Use the following formula to find the area of a circle:

$\displaystyle \text{Area}=\pi \times \text{radius}^2$

For the circle in question, plug in the given radius to find the area.

In our particular case the radius is $\displaystyle \frac{1}{5}$.

$\displaystyle \text{Area}=\pi \times \left(\frac{1}{5}\right)^2=\frac{1}{25}\pi$

When squarring a fraction we need to square both the numerator and the denominator.

$\displaystyle \pi \times \left(\frac{1}{5}\right)^2=\frac{1^2}{5^2}\pi=\frac{1\cdot 1}{5\cdot 5}\pi=\frac{1}{25}\pi$

Use the following formula to find the area of a circle:

$\displaystyle \text{Area}=\pi \times \text{radius}^2$

For the circle in question, plug in the given radius to find the area.

In this problem the known radius is $\displaystyle \sqrt5$

Now plug the radius into the area equation.

$\displaystyle \text{Area}=\pi \times \text{radius}^2$

Therefore we get,

$\displaystyle \text{Area}=\pi \times (\sqrt5)^2=5\pi$

Recall that when a square root is squared you are left with the number under the square root sign. This happens because when you square a number you are multiplying it by itself. In our case this is,

$\displaystyle (\sqrt{5})^2=\sqrt{5}\cdot \sqrt{5}$.

From here we can use the property of multiplication and radicals to rewrite our expression as follows,

$\displaystyle \sqrt{5}\cdot \sqrt{5}=\sqrt{5\cdot 5}$

and when there are two numbers that are the same under a square root sign you bring out one and the other number and square root sign go away.

$\displaystyle \sqrt{5\cdot 5}=5$

The formula for the area of a circle is

$\displaystyle \dpi{100} \pi r^{2}$

Find the radius by dividing 9 by 2:

$\displaystyle \dpi{100} \frac{9}{2}=4.5$

So the formula for area would now be:

$\displaystyle \dpi{100} \pi r^{2}=\pi (4.5)^{2}=20.25\pi \approx 63.6= 64$

To find the area, we need to determine the radius of the circle first.  

The radius is calculated as $\displaystyle r=\frac{D}{2}$, where D is the diameter.

Given that the diameter is 12 inches, the radius is $\displaystyle r=\frac{12}{2}$, or $\displaystyle r=6\ \text{inches}$.

Next, we know that the formula for the area of the circle is $\displaystyle A=\pi r^2$.

Using the radius we just found, we can find the area:

$\displaystyle A=\pi (6)^2=36\pi\ \text{inches}$

In order to solve this problem, we need to recall the formula for the area of a circle: 

$\displaystyle A= r^2\pi$

The circle in this question provides us with the radius, so we can use the formula to solve:

$\displaystyle A=3^2\pi$

Solve:

$\displaystyle A=9\pi\textup{ in}^2$