# Circle area - Examples, Exercises and Solutions

The area of the circle is, in fact, the surface that is "enclosed" within the perimeter of the circumference. It is calculated by raising the radius of the circumference $R$ to the second power and multiplying the result by -> $π$. The area of the circle is usually denoted by the letter $A$.

The formula to calculate the area of a circle is:

$A=\pi\times R\times R$

$A$ -> area of the circle
$\pi–>PI=3.14$
$R$ -> Radius of the circumference

In problems that include the radius - We will use the radius in the formula.
In problems that include the diameter - We will divide it by $2$ to obtain the radius and, only then, place the radius in the formula.
In problems that include the area and ask to find the radius - We will place the area in the formula and find the radius.

$A=π\times R\times R$

## Practice Circle area

### Exercise #1

Look at the circle in the figure:

The radius is equal to 7.

What is the area of the circle?

### Step-by-Step Solution

Remember that the formula for the area of a circle is

πR²

We replace the data we know:

π7²

π49

49π

### Exercise #2

Given the circle whose diameter is 7 cm

What is your area?

### Step-by-Step Solution

First, let's remember the formula for the area of a circle:

$\pi r^2$

In the question, we are given the diameter of the circle, but we need the radius.

It is known that the radius is actually half of the diameter, therefore:

$r=7:2=3.5$

We replace in the formula

$\pi3.5^2=12.25\pi$

### Answer

$12.25\pi$ cm².

### Exercise #3

O is the center of the circle in the diagram below.

What is its area?

### Step-by-Step Solution

Remember that the formula for the area of a circle is

πR²

We replace the data we know:

π3²

π9

### Answer

$9\pi$ cm²

### Exercise #4

Look at the circle in the figure:

The diameter of the circle is 13.

What is its area?

### Step-by-Step Solution

First, let's remember what the formula for the area of a circle is:

$S=\pi r^2$

The problem gives us the diameter, and we know that the radius is half of the diameter therefore:

$\frac{13}{2}=6.5$

We replace in the formula and solve:

$S=\pi\times6.5^2$

$S=42.25\pi$

42.25π

### Exercise #5

Look at the circle in the diagram.

AB is a chord.

Is it possible to calculate the area of the circle?

### Step-by-Step Solution

Since AB is just a chord and we know nothing else about the diameter or the radius, we cannot calculate the area of the circle.

### Answer

It is not possible.

### Exercise #1

A circle has an area of 25 cm².

What is its radius?

### Step-by-Step Solution

Area of the circle:

$S=\pi r^2$

We replace the data we know:

$25=\pi r^2$

Divide by Pi:$\frac{25}{\pi}=r^2$

Extract the root:$\sqrt{\frac{25}{\pi}}=r$

$\frac{5}{\sqrt{\pi}}=r$

### Answer

$\frac{5}{\sqrt{\pi}}$ cm

### Exercise #2

Given the semicircle:

What is the area?

### Step-by-Step Solution

Formula for the area of a circle:

$S=\pi r^2$

We complete the shape into a full circle and notice that 14 is the diameter.

A diameter is equal to 2 radii, so:$r=7$

We replace in the formula:$S=\pi\times7^2$

$S=49\pi$

24.5π

### Exercise #3

The following is a circle enclosed in a parallelogram:

All meeting points are tangent to the circle.
The circumference is 25.13.

What is the area of the zones marked in blue?

### Step-by-Step Solution

First, we add letters as reference points:

Let's observe points A and B.

We know that two tangent lines to a circle that start from the same point are parallel to each other.

Therefore:

$AE=AF=3$
$BG=BF=6$

From here we can calculate:

$AB=AF+FB=3+6=9$

Now we need the height of the parallelogram.

We know that F is tangent to the circle, so the diameter that comes out of point F will also be the height of the parallelogram.

It is also known that the diameter is equal to two radii.

It is known that the circumference of the circle is 25.13.

Formula of the circumference:$2\pi R$
We replace and solve:

$2\pi R=25.13$
$\pi R=12.565$
$R\approx4$

The height of the parallelogram is equal to two radii, that is, 8.

And from here it is possible to calculate the area of the parallelogram:

$\text{Lado }x\text{ Altura}$$9\times8\approx72$

Now, we calculate the area of the circle according to the formula:$\pi R^2$

$\pi4^2=50.26$

Now, subtract the area of the circle from the surface of the trapezoid to get the answer:

$72-56.24\approx21.73$

### Answer

$\approx21.73$

### Exercise #4

Look at the circle in the figure:



The radius of the circle is 4.

What is its area?

### Answer

$16π$

### Exercise #5

A circle has a diameter of 4 cm.

What is its area?

### Answer

$4\pi$ cm²

### Exercise #1

The center of the circle in the diagram is O.

What is the area of the circle?

### Answer

$25\pi$ cm².

### Exercise #2

Calculate the area of a circle with a radius of 5 cm.

### Answer

$25\pi$

### Exercise #3

A circle has a radius of 3 cm.

What is its area?

### Answer

$9\pi$

### Exercise #4

A circle has a radius of 6 cm.

What is its area?

### Answer

$36\pi$

### Exercise #5

A circle has a radius of 8 cm.

Calculate the area of the circle.

### Answer

$64\pi$

1. Area