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:
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:
The perimeter is measured in units of mm, cm, or meters, according to what the question states. Generally, most figures are given in units of cm. We can convert the different units of measure in the following way: 1 cm = 10 mm 1 meter = 100 cm
Now we will learn to calculate the perimeter of the most known figures. Are we ready? How is the perimeter calculated in general? All the lengths of the edges (or sides) of the figure are added together. The sum of all the edges is the perimeter.
Perimeter of the Square
a -> Side of the square In the square, all sides are equal, therefore, its perimeter will be 4 times the side a. We will multiply the side of the square by 4.
Join Over 30,000 Students Excelling in Math!
Endless Practice, Expert Guidance - Elevate Your Math Skills Today
Test your knowledge
Question 1
Look at the circle in the figure below.
The radius of the circle equals 5.
What is its perimeter?
Incorrect
Correct Answer:
\( 10\pi \)
Question 2
Look at the circle in the figure below.
The radius of the circle equals 7.
What is its perimeter?
Incorrect
Correct Answer:
\( 14\pi \)
Question 3
Look at the circle in the figure.
Given that its radius is equal to 3, what is its circumference?
Incorrect
Correct Answer:
\( 6\pi \)
Perimeter of the Rectangle
Let's add up the sides of the rectangle. The opposite sides are equal.
Let's add up all the sides of the triangle. In an isosceles triangle it is enough to know the length of the base and one of the two equal sides. In an equilateral triangle it is enough to know the length of one side.
The key to calculating the perimeter of these figures is to add up absolutely all the sides without forgetting any of them. Start on one side, follow the entire round and stop when you reach the same side from which you started.
Let's see an example:
The area is: 4+4+4+5+2+8+2+3=32
Test your knowledge
Question 1
Calculate the perimeter of the trapezoid below:
Incorrect
Correct Answer:
30
Question 2
Calculate the perimeter of the trapezoid below:
Incorrect
Correct Answer:
48
Question 3
Look at the circle in the figure below.
The radius of the circle is equal to 8.
What is its perimeter?
Incorrect
Correct Answer:
\( 16\pi \)
What is the difference between perimeter and surface area?
The perimeter is measured in two-dimensional figures that do not have volume, for example, a rectangle
In contrast, the surface area is measured in three-dimensional figures that do have volume, for example, a cylinder or cube.
Examples and exercises with solutions for the perimeter of the parallelogram
Exercise #1
Calculate the perimeter of the trapezoid according to the following data:
Video Solution
Step-by-Step Solution
To solve this problem, we'll calculate the perimeter of the trapezoid by summing the lengths of all its sides. The steps are as follows:
List the lengths of the sides: the bases are 10 and 12, and the two non-parallel sides are each 7.
Apply the perimeter formula for a trapezoid: P=a+b+c+d.
Substitute the given values into the formula: P=10+12+7+7.
Calculate the sum: P=10+12+7+7=36.
Therefore, the perimeter of the trapezoid is 36.
This matches the correct answer choice from the provided options.
Answer
36
Exercise #2
Calculate the perimeter of the trapezoid below:
Step-by-Step Solution
To solve this problem, we'll calculate the perimeter of the trapezoid by summing the lengths of its sides:
Step 1: Identify the side lengths of the trapezoid:
Top side =10, Bottom side =5, Left side =10, Right side =11.
Step 2: Apply the perimeter formula:
The formula for the perimeter P of a trapezoid is P=a+b+c+d.
Step 3: Perform the calculations:
Substitute the given lengths into the formula: P=10+5+10+11=36.
Therefore, the perimeter of the trapezoid is 36.
Answer
36
Examples and exercises with solutions for the perimeter of a trapezoid
Exercise #1
Calculate the perimeter of the trapezoid according to the following data:
Video Solution
Step-by-Step Solution
To solve this problem, we'll calculate the perimeter of the trapezoid by summing the lengths of all its sides. The steps are as follows:
List the lengths of the sides: the bases are 10 and 12, and the two non-parallel sides are each 7.
Apply the perimeter formula for a trapezoid: P=a+b+c+d.
Substitute the given values into the formula: P=10+12+7+7.
Calculate the sum: P=10+12+7+7=36.
Therefore, the perimeter of the trapezoid is 36.
This matches the correct answer choice from the provided options.
Answer
36
Exercise #2
Calculate the perimeter of the trapezoid below:
Step-by-Step Solution
To solve this problem, we'll calculate the perimeter of the trapezoid by summing the lengths of its sides:
Step 1: Identify the side lengths of the trapezoid:
Top side =10, Bottom side =5, Left side =10, Right side =11.
Step 2: Apply the perimeter formula:
The formula for the perimeter P of a trapezoid is P=a+b+c+d.
Step 3: Perform the calculations:
Substitute the given lengths into the formula: P=10+5+10+11=36.
Therefore, the perimeter of the trapezoid is 36.
Answer
36
Examples and exercises with solutions for the perimeter of the triangle
Exercise #1
Calculate the perimeter of the trapezoid according to the following data:
Video Solution
Step-by-Step Solution
To solve this problem, we'll calculate the perimeter of the trapezoid by summing the lengths of all its sides. The steps are as follows:
List the lengths of the sides: the bases are 10 and 12, and the two non-parallel sides are each 7.
Apply the perimeter formula for a trapezoid: P=a+b+c+d.
Substitute the given values into the formula: P=10+12+7+7.
Calculate the sum: P=10+12+7+7=36.
Therefore, the perimeter of the trapezoid is 36.
This matches the correct answer choice from the provided options.
Answer
36
Exercise #2
Calculate the perimeter of the trapezoid below:
Step-by-Step Solution
To solve this problem, we'll calculate the perimeter of the trapezoid by summing the lengths of its sides:
Step 1: Identify the side lengths of the trapezoid:
Top side =10, Bottom side =5, Left side =10, Right side =11.
Step 2: Apply the perimeter formula:
The formula for the perimeter P of a trapezoid is P=a+b+c+d.
Step 3: Perform the calculations:
Substitute the given lengths into the formula: P=10+5+10+11=36.
Therefore, the perimeter of the trapezoid is 36.
Answer
36
Examples and exercises with solutions for the perimeter of the rectangle
Exercise #1
Calculate the perimeter of the trapezoid according to the following data:
Video Solution
Step-by-Step Solution
To solve this problem, we'll calculate the perimeter of the trapezoid by summing the lengths of all its sides. The steps are as follows:
List the lengths of the sides: the bases are 10 and 12, and the two non-parallel sides are each 7.
Apply the perimeter formula for a trapezoid: P=a+b+c+d.
Substitute the given values into the formula: P=10+12+7+7.
Calculate the sum: P=10+12+7+7=36.
Therefore, the perimeter of the trapezoid is 36.
This matches the correct answer choice from the provided options.
Answer
36
Exercise #2
Calculate the perimeter of the trapezoid below:
Step-by-Step Solution
To solve this problem, we'll calculate the perimeter of the trapezoid by summing the lengths of its sides:
Step 1: Identify the side lengths of the trapezoid:
Top side =10, Bottom side =5, Left side =10, Right side =11.
Step 2: Apply the perimeter formula:
The formula for the perimeter P of a trapezoid is P=a+b+c+d.
Step 3: Perform the calculations:
Substitute the given lengths into the formula: P=10+5+10+11=36.
Therefore, the perimeter of the trapezoid is 36.
Answer
36
Do you know what the answer is?
Question 1
Look at the circle in the figure below.
The radius of the circle equals 5.
What is its perimeter?
Incorrect
Correct Answer:
\( 10\pi \)
Question 2
Look at the circle in the figure below.
The radius of the circle equals 7.
What is its perimeter?
Incorrect
Correct Answer:
\( 14\pi \)
Question 3
Look at the circle in the figure.
Given that its radius is equal to 3, what is its circumference?
