Circumference - Examples, Exercises and Solutions

What is the perimeter?

The perimeter indicates the distance we will walk if we start from a certain point, complete a full lap, and return exactly to the starting point.
For example, if we are asked what the perimeter of the waist is, we will take a tape measure and measure the perimeter from a certain point until completing a full lap and returning to the same point from which we started the measurement.
It works exactly the same way in mathematics. The perimeter of any shape is the distance from a specific point back to it after having completely surrounded it.
If this is our figure:

What is the perimeter

Its perimeter will be the distance we cover if we travel along its line from a certain point, and return to it after making a full lap. Imagine that you are surrounding the figure:


Practice Circumference

Exercise #1

Given the parallelogram:

101010777AAABBBDDDCCC

Calculate the perimeter of the parallelogram.

Video Solution

Step-by-Step Solution

As in a parallelogram each pair of opposite sides are equal and parallel,

It is possible to argue that:

AC=BD=7 AC=BD=7

AB=CD=10 AB=CD=10

Now we can calculate the perimeter of the parallelogram by adding all its sides:

10+10+7+7=20+14=34 10+10+7+7=20+14=34

Answer

34

Exercise #2

Given the parallelogram:

666444AAABBBDDDCCC

Calculate the perimeter of the parallelogram.

Video Solution

Step-by-Step Solution

As in a parallelogram every pair of opposite sides are equal:

AB=CD=6,AC=BD=4 AB=CD=6,AC=BD=4

The perimeter of the parallelogram is equal to the sum of all sides together:

4+4+6+6=8+12=20 4+4+6+6=8+12=20

Answer

20

Exercise #3

Look at the circle in the figure.

What is its circumference if its radius is equal to 6?

6

Video Solution

Step-by-Step Solution

Formula of the circumference:

P=2πr P=2\pi r

We replace the data in the formula:

P=2×6×π P=2\times6\times\pi

P=12π P=12\pi

Answer

12π 12\pi

Exercise #4

Look at the rectangle below.

Side AB is 4.8 cm long and side AD has a length of 12 cm.

What is the perimeter of the rectangle?
4.84.84.8121212AAABBBCCCDDD

Video Solution

Step-by-Step Solution

In the drawing, we have a rectangle, although it is not placed in its standard form and is slightly rotated,
but this does not affect that it is a rectangle, and it still has all the properties of a rectangle.
 
The perimeter of a rectangle is the sum of all its sides, that is, to find the perimeter of the rectangle we will have to add the lengths of all the sides.
We also know that in a rectangle the opposite sides are equal.
Therefore, we can use the existing sides to complete the missing lengths.
 
4.8+4.8+12+12 =
33.6 cm

Answer

33.6 cm

Exercise #5

Look at the following rectangle:

AAABBBCCCDDD95

Find its perimeter.

Video Solution

Step-by-Step Solution

Since in a rectangle all pairs of opposite sides are equal:

AD=BC=5 AD=BC=5

AB=CD=9 AB=CD=9

Now we calculate the perimeter of the rectangle by adding the sides:

5+5+9+9=10+18=28 5+5+9+9=10+18=28

Answer

28

Exercise #1

Look at the circle in the figure:

444

Its radius is equal to 4.

What is its circumference?

Video Solution

Step-by-Step Solution

The formula for the circumference is equal to:

2πr 2\pi r

Answer

Exercise #2

Given the triangle:

777111111131313

What is its perimeter?

Video Solution

Step-by-Step Solution

The perimeter of a triangle is equal to the sum of all its sides together:

11+7+13=11+20=31 11+7+13=11+20=31

Answer

31

Exercise #3

Look at the triangle below:

666888101010

What is the perimeter of the triangle?

Video Solution

Step-by-Step Solution

The perimeter of the triangle is equal to the sum of all sides together, therefore:

6+8+10=14+10=24 6+8+10=14+10=24

Answer

24

Exercise #4

What is the perimeter of the trapezoid in the figure?

444555999666

Video Solution

Step-by-Step Solution

To find the perimeter we will add all the sides:

4+5+9+6=9+9+6=18+6=24 4+5+9+6=9+9+6=18+6=24

Answer

24

Exercise #5

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

888OOO What is its circumference?

Video Solution

Step-by-Step Solution

We use the formula:P=2πr P=2\pi r

We replace the data in the formula:P=2×8π P=2\times8\pi

P=16π P=16\pi

Answer

16π 16\pi cm

Exercise #1

Look at the trapezoid in the figure.

The long base is 1.5 times longer than the short base.

Find the perimeter of the trapezoid.

222333555

Video Solution

Step-by-Step Solution

First, we calculate the long base from the existing data:

Multiply the short base by 1.5:

5×1.5=7.5 5\times1.5=7.5

Now we will add up all the sides to find the perimeter:

2+5+3+7.5=7+3+7.5=10+7.5=17.5 2+5+3+7.5=7+3+7.5=10+7.5=17.5

Answer

17.5

Exercise #2

Given the following rectangle:

AAABBBCCCDDDEEEFFF4615

What is the perimeter of the rectangle ABCD?

Video Solution

Step-by-Step Solution

Given that in the smaller rectangle ED=CF=4 (each pair of opposite sides in the rectangle are equal)

Now we can calculate in the rectangle ABCD that BC=6+4=10

Now we can state in the rectangle ABCD that BC=AD=10

Calculate the perimeter of the rectangle by adding all the sides:

DC=AB=15

The perimeter of the rectangle ABCD is equal to:

10+10+15+15=20+30=50 10+10+15+15=20+30=50

Answer

50

Exercise #3

Below is a rectangle composed of two squares.

666AAABBBCCCDDDEEEFFF

What is its perimeter?

Video Solution

Step-by-Step Solution

In a square, all sides are equal. Therefore:
AB+BC+CD+DE+EF+FA=6 AB+BC+CD+DE+EF+FA=6

Thus, we find out what the side AC is equal to:

AC=AB+BC AC=AB+BC

AB=6+6=12 AB=6+6=12

In a rectangle, we know that the opposite sides are equal to each other, therefore:

AB=FD=12 AB=FD=12

Therefore, the formula for the perimeter of the rectangle will look like this:

2×AB+2×CD 2\times AB+2\times CD

We replace the data:

2×12+2×6= 2\times12+2\times6=

24+12=36 24+12=36

Answer

36

Exercise #4

Given the following rectangle:

AAABBBCCCDDDEEEFFF710

What is the perimeter of the rectangle ABCD?

Video Solution

Step-by-Step Solution

In the statement, we have two rectangles that are connected by a common side,

The left quadrilateral, AEFD, has a known side - AD

The right quadrilateral, EBCF, also has only one known side: FC

In the question, we are asked for the perimeter of the rectangle ABCD,

For this, we need its sides, and since the opposite sides in a rectangle are equal, we need at least two adjacent sides.

We are given the side AD, but the side DC is only partially given.

We have no way of finding the missing part: DF, so we have no way of answering the question.

This is the solution!

Answer

It is not possible to know

Exercise #5

Given an equilateral triangle:

555

What is its perimeter?

Video Solution

Step-by-Step Solution

Since the triangle is equilateral, that is, all sides are equal to each other.

The perimeter of the triangle is equal to the sum of all sides together, the perimeter of the triangle in the drawing is equal to:

5+5+5=15 5+5+5=15

Answer

15

Topics learned in later sections

  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. Area
  8. Area of a circle