Area of the square - Examples, Exercises and Solutions

In this article, we will learn what area is, and understand how it is calculated for each shape, in the most practical and simple way there is.
Shall we start?

What is the area?

Area is the definition of the size of something. In mathematics, which is precisely what interests us now, it refers to the size of some figure.
In everyday life, you have surely heard about area in relation to the surface of an apartment, plot of land, etc.
In fact, when they ask what the surface area of your apartment is, they are asking about its size and, instead of answering with words like "big" or "small" we can calculate its area and express it with units of measure. In this way, we can compare different sizes.

Units of measurement of area

Large areas such as apartments are usually measured in meters, therefore, the unit of measurement will be m2 m^2 square meter.
On the other hand, smaller figures are generally measured in centimeters, that is, the unit of measurement for the area will be cm2 cm^2 square centimeter.
Remember:
Units of measurement for the area in cm=>cm2 cm => cm^2
Units of measurement for the area m=>m2 m=>m^2

Suggested Topics to Practice in Advance

  1. Square

Practice Area of the square

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

What is the area of the given triangle?

555999666

Video Solution

Step-by-Step Solution

This question is a bit confusing. We need start by identifying which parts of the data are relevant to us.

Remember the formula for the area of a triangle:

A1- How to find the area of a triangleThe height is a straight line that comes out of an angle and forms a right angle with the opposite side.

In the drawing we have a height of 6.

It goes down to the opposite side whose length is 5.

And therefore, these are the data points that we will use.

We replace in the formula:

6×52=302=15 \frac{6\times5}{2}=\frac{30}{2}=15

Answer

15

Exercise #3

Given the trapezoid:

999121212555AAABBBCCCDDDEEE

What is the area?

Video Solution

Step-by-Step Solution

Formula for the area of a trapezoid:

(base+base)2×altura \frac{(base+base)}{2}\times altura

We substitute the data into the formula and solve:

9+122×5=212×5=1052=52.5 \frac{9+12}{2}\times5=\frac{21}{2}\times5=\frac{105}{2}=52.5

Answer

52.5

Exercise #4

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 #5

Given the rhombus in the drawing:

444777

What is the area?

Video Solution

Step-by-Step Solution

Let's remember that there are two ways to calculate the area of a rhombus:

The first is the side times the height of the side.

The second is diagonal times diagonal divided by 2.

Since we are given both diagonals, we calculate it the second way:

7×42=282=14 \frac{7\times4}{2}=\frac{28}{2}=14

Answer

14

Exercise #1

Look at the deltoid in the figure:

777444

What is its area?

Video Solution

Step-by-Step Solution

Initially, let's remember the formula for the area of a kite

Diagonal1×Diagonal22 \frac{Diagonal1\times Diagonal2}{2}

Both pieces of information already exist, so we can place them in the formula:

(4*7)/2

28/2

14

Answer

14

Exercise #2

Shown below is the deltoid ABCD.

The diagonal AC is 8 cm long.

The area of the deltoid is 32 cm².

Calculate the diagonal DB.

S=32S=32S=32888AAABBBCCCDDD

Video Solution

Step-by-Step Solution

First, we recall the formula for the area of a kite: multiply the lengths of the diagonals by each other and divide this product by 2.

We substitute the known data into the formula:

 8DB2=32 \frac{8\cdot DB}{2}=32

We will reduce the 8 and the 2:

4DB=32 4DB=32

Divide by 4

DB=8 DB=8

Answer

8 cm

Exercise #3

The trapezoid ABCD is shown below.

AB = 2.5 cm

DC = 4 cm

Height (h) = 6 cm

Calculate the area of the trapezoid.

2.52.52.5444h=6h=6h=6AAABBBCCCDDD

Video Solution

Step-by-Step Solution

First, let's remind ourselves of the formula for the area of a trapezoid:

A=(Base + Base) h2 A=\frac{\left(Base\text{ }+\text{ Base}\right)\text{ h}}{2}

We substitute the given values into the formula:

(2.5+4)*6 =
6.5*6=
39/2 = 
19.5

Answer

1912 19\frac{1}{2}

Exercise #4

Calculate the area of the triangle ABC using the data in the figure.

121212888999AAABBBCCCDDD

Video Solution

Step-by-Step Solution

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

(the side * the height that descends to the side) /2

 

In the question, we have three pieces of data, but one of them is redundant!

We only have one height, the line that forms a 90-degree angle - AD,

The side to which the height descends is CB,

Therefore, we can use them in our calculation:

CB×AD2 \frac{CB\times AD}{2}

8×92=722=36 \frac{8\times9}{2}=\frac{72}{2}=36

Answer

36 cm²

Exercise #5

Calculate the area of the right triangle below:

101010666888AAACCCBBB

Video Solution

Step-by-Step Solution

As we see that AB is perpendicular to BC and forms a 90-degree angle

It can be argued that AB is the height of the triangle.

Then we can calculate the area as follows:

AB×BC2=8×62=482=24 \frac{AB\times BC}{2}=\frac{8\times6}{2}=\frac{48}{2}=24

Answer

24 cm²

Exercise #1

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 #2

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 #3

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 #4

Calculate the area of the following triangle:

444555AAABBBCCCEEE

Video Solution

Step-by-Step Solution

The formula for calculating the area of a triangle is:

(the side * the height from the side down to the base) /2

That is:

BC×AE2 \frac{BC\times AE}{2}

Now we replace the existing data:

4×52=202=10 \frac{4\times5}{2}=\frac{20}{2}=10

Answer

10

Exercise #5

What is the area of the trapezoid in the figure?

777151515222AAABBBCCCDDDEEE

Video Solution

Step-by-Step Solution

We use the formula to calculate the area of a trapezoid: (base+base) multiplied by the height divided by 2:

(AB+DC)×BE2 \frac{(AB+DC)\times BE}{2}

(7+15)×22=22×22=442=22 \frac{(7+15)\times2}{2}=\frac{22\times2}{2}=\frac{44}{2}=22

Answer

22 22 cm².

Topics learned in later sections

  1. Area of a square