Calculating the Area of a Rectangle

🏆Practice area of a rectangle

How Do You Calculate the Area of a Rectangle?

Compared to other geometric figures, the rectangle is one of the simplest to work with.

One of the most frequent questions that comes up in exams is related to how to calculate the area of the rectangle.

Before we focus on it, let's do a brief review.

The formula for calculating the area of a rectangle is as follows:

A1 -Base DC x Height AD = Area of the rectangle

Base DC×Height AD=Area of rectangle Base~DC\times Height~AD=Area~of~rectangle

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Test yourself on area of a rectangle!

einstein

Look at the rectangle ABCD below.

Side AB is 6 cm long and side BC is 4 cm long.

What is the area of the rectangle?
666444AAABBBCCCDDD

Practice more now

Calculating the area of a rectangle is very similar to the formula for calculating the area of a square.

Characteristics of a Rectangle

A rectangle is a quadrilateral that is characterized by the following:

All of its angles are right angles (90º).

Its opposite sides have the same length.

If you are interested in this article, you may also be interested in the following articles:

Rectangle

The perimeter of a rectangle

Rectangles of Equivalent Area and Perimeter

In Tutorela website, you will find a variety of other helpful articles about mathematics!


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How to Calculate the Area of a Rectangle: A Comprehensive Explanation with Examples

Base × Height

Example 1

Let's imagine a rectangle with a base of 5 cm 5~cm and a height of 10 cm 10~cm.
In this case, to calculate the area of the rectangle we will have to multiply the base by the height, resulting in 50 cm 50~cm.

Area of a rectangle:

A2 - How to calculate the area of a rectangle


Note that no matter how long the sides of the rectangle are, the formula for calculating its area will always be the same.

Do you know what the answer is?

Example 2

Let's take the rectangle from the previous example, but this time we'll rotate it. This is an insignificant change since, so long as you have correctly identified the base and the height (base = 5 cm 5~cm and height = 10 cm 10~cm), the result will be the same.

v -How to calculate the area of a rectangle in verticlal


Example 3

Let's take the same rectangle again, but this time we rotae it diagonally.
The measurements are still the same—only its orientation has changed.

Do you think the area of the rectangle has changed?
No,
its area is still 50 cm 50~cm. This is the result we have obtained after multiplying its base by its height.

A4 - How to calculate the area of a diagonal rectangle


Check your understanding

Exercises in Calculating the Area of a Rectangle

Exercise 1

Below is a rectangle with the following characteristics:

Base: 35 cm 35~cm

Height: 70 cm 70~cm

Task:

What is the area of the rectangle?

Solution:

A5 - calculate the area of a rectangle

Answer: 2450cm2 2450\operatorname{cm}²


Exercise 2

Below is the rectangle ABCD ABCD with the following characteristics:

Base: 44 cm 44~cm

Height: 88 cm 88~cm

Another rectangle (EFGH EFGH )is inside the rectangle ABCD ABCD and has the following characteristics:

Base: 11 cm 11~cm

Height: 33 cm 33~cm

Task:

What is the difference in area between the two rectangles?

Solution:

A6- What is the difference in area between the two rectangles

Rectangle ABCD ABCD

Base: AB=44 cm AB = 44~cm

Height: AD=88 cm AD = 88~cm

44×88=3872 cm2 44\times88=3872~cm²

Rectangle EFGH EFGH

Base: EF=11 cm EF = 11~cm

Height: EG=33 cm EG = 33~cm

11×33=363 cm2 11\times33=363~cm²

ABCDEFGH=3872363=3509 cm2 ABCD-EFGH=3872-363=3509~cm²

Answer: 3509cm2 3509\operatorname{cm}²


Do you think you will be able to solve it?

Exercise 3

Below is the rectangle ABCD ABCD with an area equal to 30 cm2 30~cm² . The side AB AB is equal to 5 cm 5~cm .

rectangle ABCD of 30cm².

Task:

What is the length of the side BC BC ?

Solution:

First, substitute the given value into the formula to calculate the area of the rectangle.

5×X=30 5\times X=30

Divide the equation by 5 5.

30:5=X 30:5=X

6=X 6=X

Answer: 6 cm 6~cm


Exercise 4

Below is the rectangle ABCD ABCD . Side AB AB has a length of 10 cm 10~cm and side BC BC has a length of 2.5 cm 2.5~cm .

Exercise 4- the rectangle ABCD

Task:

What is the area of the rectangle?

Solution:

First, substitute the values into the formula for the area of a rectangle.

10×2.5 10\times2.5

And solve:

10×2.5=25 cm2 10\times2.5=25~cm²

Answer: 25 cm2 25~cm²


Test your knowledge

Exercise 5

Below is a rectangle and an isosceles right triangle:

the rectangle and the isosceles right triangle

Homework:

What is the area of the rectangle?

Solution:

To find the missing side, we will use the Pythagorean Theorem on the upper triangle.

Since the triangle is isosceles, we know that the length of the two sides are both 7 7 .

Therefore, substituting the given values into the formula of the Pythagorean Theorem we get A2+B2=C2A^2+B^2=C^2.

72+72=49+49=98 7^2+7^2=49+49=98

Therefore, the measure of the side AB AB is 98 \sqrt{98} .

Answer:

The area of the rectangle is the product of its base and height, therefore:

98×10=98.9999u2 \sqrt{98}\times10=98.99\approx99u²


Exercise 6

Below is the rectangle ABCD ABCD .

BC=X BC=X and the side AB AB is 4 cm 4~cm longer than the side BC BC .

The area of the triangle ABC ABC is 8X cm2 8X~cm² .

A9 - rectangle ABCD

Task:

Calculate the side BC BC .

Solution:

To find the side BC BC , we will use the given value and place it in the formula to calculate the area of the triangle ABC \triangle ABC .

Formula to calculate the area of the triangle:

ABC= \triangle ABC= ABC=AB×BC2 \text{ABC}=\frac{AB\times BC}{2}

AB=X+4 AB=X+4

(Since the side AB AB is 4 4 longer than the side BC BC )

BC=X BC=X

A=8X A=8X

Area ABC ABC

AreaABC=(X+4)×X2=8X1 A\text{reaABC}=\frac{(X+4)\times X}{2}=\frac{8X}{1} (we multiply crosswise)

16X=X(X+4) 16X=X(X+4) /: X X (divided byX X )

16=X+4 16=X+4

X=12 X=12

Answer:

Side BC BC is equal to 12 cm 12~cm .


Do you know what the answer is?

Exercise 7

Below is the rectangle ABCD ABCD .

BC=5cm BC=5\operatorname{cm}

The perimeter of the rectangle =40 cm = 40~cm .

Exercise 7 the rectangle ABCD

Task:

What is the area of the rectangle?

Solution:

Find the area of the rectangle given that BC=5 BC=5 .

AD=5 AD=5 (opposite sides are equal in a rectangle)

PBCAD=4055=30P-BC-AD=40-5-5=30

AB+DC=30 AB+DC=30

AB=15 AB=15

A=ABBC=155=75 A=AB\cdot BC=15\cdot5=75

Answer:

75cm2 75\operatorname{cm}²


A Brief Reminder

How do you calculate the area and perimeter of a rectangle?

For the area, multiply the base by the height.

For the perimeter, add the length of the four sides together.


Check your understanding

How do you calculate the area of a rectangle and a square?

For the area of the rectangle, multiply the base by the height.

For the area of the square, multiply a side by another side.


What is the formula for finding the perimeter of a rectangle?

For the perimeter, we add the length of the four sides together.


So what do students find tricky when it comes to applying the formula for calculating the area of a rectangle?

The formula for calculating the area of a rectangle is one of the easiest to understand—simply memorize and apply. However, the real problem is not so much understanding it, but applying it.


Why?

This is because, in many instances, the exercises do not provide you with all the necessary values and you will have to work them out for yourself. To do this, you need to know all of the specific characteristics of a rectangle.


Do you think you will be able to solve it?

Learning Tips and Tricks

Getting help from a private tutor

Students who experience difficulty should find a way to remedy their problems. If you feel like you need help keeping up with the pace of learning at school, seeking the guidance of a private math is a great option.

Falling behind? This can cause you unnecessary stress, prevent you from making progress, and ultimately cause you to do poorly on your exams. Don't let it get to that point!


They are not 'problems', they are 'puzzles'!

The word 'problem' generates a lot of problems itself among many students. Even before we read the statement, a feeling of stress and uncertainty can come over us.
One of the best ways to reduce this stress when solving a problem is to see it in a different light: instead of problem, call it a puzzle!

Why?

This is because a 'problem' is understood as something complicated and difficult that we have to face.
However, a 'puzzle' or 'riddle' has a more positive connotation—it is a mental challenge rather than a difficulty.


Test your knowledge

What to do when you get a low score on an exam?

Did you study hard for a geometry exam that contained questions on how to calculate the area of a rectangle and didn't get the grade you were hoping for? Accept the disappointment and give yourself a few hours, or even a day, to be in a bad mood.
That said, remember that the course is not over yet and that you still have many more exams and quizzes that present other opportunities to raise your scores.
Besides, a bad grade can teach you many things. For example, it can help you understand flaws in your your study skills, your learning habits, and your mastery of certain subjects.

A little tip: Read the entire exam very carefully.

What does this mean? Try to understand why you didn't do well.

For example:

  • You have made many small calculation errors that have resulted in lost points.
    Solution: read each question several times and rethink your calculations.
  • You were deducted 2.5 points for an exercise that you could not finish.
    Solution: practice with as many exercises as possible to shorten your answering time.
  • You took the exam without having prepared sufficiently due to lack of time.
    Solution: make an organized study plan before each exam.

"I don't study for exams because they don't affect the average."

Do you have a geometry exam coming up on rectangles and how to calculate their area? It's important that you study!
First, even though the formula for calculating the area of a rectangle is simple (it's a simple multiplication), it will not always provide you with all the data and you will have to figure it out for yourself from the values provided to you.

To be able to do this, you must know all of the characteristics of each geometric shape and, therefore, need to study the topic thoroughly!

Why? Because this forces you to practice the subject material in a comprehensive way.


Many students are intimidated by midterm exams and would prefer to have only final exams

You need to embrace exams and see them as an opportunity to consolidate the knowledge you have acquired on the subject—enjoy the small achievements and try to increase your average.
Unlike a final exam, which includes many topics that you have studied throughout the term, a midterm only focuses on a single topic.

For example:

Geometric shapes, such as the rectangle.


Do you know what the answer is?

Sample study plan for a geometry exam on the rectangle

How should you prepare for the exam? First, plan the days and times you will study.
As an elementary, middle, or high school student, you must divide your time between many subjects, assignments, midterms, and finals.
Therefore, you should create an organized study plan that you can commit to.

Here is an example:

  • Study days: 7
  • Study on weekends: - yes or no?
  • Private tutoring: - yes or no?

Example of a study day: Monday

  • 16.00-18.00: Practice calculating the area of rectangles.
  • 18.00-20.00: Practice with different tests involving all shapes.

Check your understanding

Some tips for studying for the exam

  • Turn off your cell phone before you start studying.
  • Don't check the solutions, but rather try to solve the problem independently.
  • Do not ignore your mistakes, learn from them!
  • Give yourself positive reinforcement for each day of study that went well.
  • Be honest with yourself—you should know what you do best and what subjects you need to reinforce.

Breaking the myth: "mathematics is a subject only for students who are good with numbers"

One of the most mistaken assumptions is that there are students who are good at mathematics and students who are not.
It is true that some may find it easier to deal with data, shapes, equations, and variables, but this does not mean that those students who need a little more time will not be able to pass the subject or get good grades.

There are students who do not manage to advance at the pace set by the class and therefore stop working hard and fall behind.
As a student, you should focus on having the highest possible average in your final exams and in the EVAU.


Do you think you will be able to solve it?

So, what should you do to get a good grade in mathematics?

  • Pay attention in all math classes
  • Always do your homework!
  • Ask your teacher for supplementary material for the subjects you feel you are weakest in.
  • Don't be shy—a private tutor can be a great help!
  • Try to study hard before each exam.

Test your knowledge

examples with solutions for area of a rectangle

Exercise #1

Look at the rectangle ABCD below.

Side AB is 6 cm long and side BC is 4 cm long.

What is the area of the rectangle?
666444AAABBBCCCDDD

Video Solution

Step-by-Step Solution

Remember that the formula for the area of a rectangle is width times height

 

We are given that the width of the rectangle is 6

and that the length of the rectangle is 4

 Therefore we calculate:

6*4=24

Answer

24 cm²

Exercise #2

Given the following rectangle:

666999AAABBBDDDCCC

Find the area of the rectangle.

Video Solution

Step-by-Step Solution

We will use the formula to calculate the area of a rectangle: length times width

9×6=54 9\times6=54

Answer

54

Exercise #3

The width of a rectangle is equal to 42 4^2 cm and its length is 5 5 cm.

Calculate the area of the rectangle.

Video Solution

Step-by-Step Solution

We use the formula to calculate a rectangle: length times width:

According to the existing data:

42×5=S 4^2\times5^=S

S=16×5 S=16\times5

S=80 S=80

Answer

80

Exercise #4

The area of the rectangle below is equal to 63.

AC = 7

How long is side AB?

777AAABBBDDDCCC63

Video Solution

Step-by-Step Solution

We use the formula to calculate a rectangle: length times width:

AB×AC=S AB\times AC=S

We place the existing data into the formula:

AB×7=63 AB\times7=63

7AB=63 7AB=63

We divide both sides by 7:

AB=9 AB=9

Answer

9

Exercise #5

The area of a rectangle is equal to 8.

Calculate the perimeter of the rectangle.

888444222AAABBBDDDCCC

Video Solution

Step-by-Step Solution

According to the properties of the rectangle, all pairs of opposite sides are equal.

AB=CD=8 AB=CD=8

AC=BD=2 AC=BD=2

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

4+4+2+2=8+4=12 4+4+2+2=8+4=12

Answer

12

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