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 RR to the second power and multiplying the result by -> π π . The area of the circle is usually denoted by the letter A A .

The formula to calculate the area of a circle is:

A=π×R×R A=\pi\times R\times R

A A -> area of the circle
π>PI=3.14 \pi–>PI=3.14
R 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 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.

A1 - The formula to calculate the area of a circle

A=π×R×R A=π\times R\times R

Suggested Topics to Practice in Advance

  1. Circle
  2. Diameter
  3. The Circumference of a Circle
  4. The Center of a Circle
  5. Radius
  6. How is the radius calculated using its circumference?
  7. Perimeter

Practice Circle area

Exercise #1

Look at the circle in the figure:

777

The radius is equal to 7.

What is the area of the circle?

Video Solution

Step-by-Step Solution

Remember that the formula for the area of a circle is

πR²

 

We replace the data we know:

π7²

π49

Answer

49π

Exercise #2

Given the circle whose diameter is 7 cm

What is your area?

777

Video Solution

Step-by-Step Solution

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

 πr2 \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 r=7:2=3.5

We replace in the formula

π3.52=12.25π \pi3.5^2=12.25\pi

Answer

12.25π 12.25\pi cm².

Exercise #3

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

What is its area?

333OOO

Video Solution

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

9π 9\pi cm²

Exercise #4

Look at the circle in the figure:

131313

The diameter of the circle is 13.

What is its area?

Video Solution

Step-by-Step Solution

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

S=πr2 S=\pi r^2

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

132=6.5 \frac{13}{2}=6.5

We replace in the formula and solve:

S=π×6.52 S=\pi\times6.5^2

S=42.25π S=42.25\pi

Answer

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?

555AAABBB

Video Solution

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?

Video Solution

Step-by-Step Solution

Area of the circle:

S=πr2 S=\pi r^2

We replace the data we know:

25=πr2 25=\pi r^2

Divide by Pi:25π=r2 \frac{25}{\pi}=r^2

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

5π=r \frac{5}{\sqrt{\pi}}=r

Answer

5π \frac{5}{\sqrt{\pi}} cm

Exercise #2

Given the semicircle:
141414
What is the area?

Video Solution

Step-by-Step Solution

Formula for the area of a circle:

S=πr2 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 r=7

We replace in the formula:S=π×72 S=\pi\times7^2

S=49π S=49\pi

Answer

24.5π

Exercise #3

The following is a circle enclosed in a parallelogram:

36

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

What is the area of the zones marked in blue?

Video Solution

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

From here we can calculate:

AB=AF+FB=3+6=9 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:2πR 2\pi R
We replace and solve:

2πR=25.13 2\pi R=25.13
πR=12.565 \pi R=12.565
R4 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:

Lado x Altura \text{Lado }x\text{ Altura} 9×872 9\times8\approx72

Now, we calculate the area of the circle according to the formula:πR2 \pi R^2

π42=50.26 \pi4^2=50.26

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

7256.2421.73 72-56.24\approx21.73

Answer

21.73 \approx21.73

Exercise #4

Look at the circle in the figure:

444

The radius of the circle is 4.

What is its area?

Video Solution

Answer

16π 16π

Exercise #5

A circle has a diameter of 4 cm.

What is its area?

444

Video Solution

Answer

4π 4\pi cm²

Exercise #1

The center of the circle in the diagram is O.

What is the area of the circle?

555OOO

Video Solution

Answer

25π 25\pi cm².

Exercise #2

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

555

Video Solution

Answer

25π 25\pi

Exercise #3

A circle has a radius of 3 cm.

333

What is its area?

Video Solution

Answer

9π 9\pi

Exercise #4

A circle has a radius of 6 cm.

6

What is its area?

Video Solution

Answer

36π 36\pi

Exercise #5

A circle has a radius of 8 cm.

888

Calculate the area of the circle.

Video Solution

Answer

64π 64\pi

Topics learned in later sections

  1. Area