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?

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?

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.

Large areas such as apartments are usually measured in meters, therefore, the unit of measurement will be $m^2$ square meter.

On the other hand, smaller figures are generally measured in centimeters, that is, the unit of measurement for the area will be $cm^2$ square centimeter.

**Remember:**

Units of measurement for the area in $cm => cm^2$

Units of measurement for the area $m=>m^2$

Question 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?

Question 2

What is the area of the given triangle?

Question 3

Given the trapezoid:

What is the area?

Question 4

Look at the circle in the figure:

The radius is equal to 7.

What is the area of the circle?

Question 5

Given the rhombus in the drawing:

What is the area?

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?

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

24 cm²

What is the area of the given triangle?

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:

The 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:

$\frac{6\times5}{2}=\frac{30}{2}=15$

15

Given the trapezoid:

What is the area?

Formula for the area of a trapezoid:

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

We substitute the data into the formula and solve:

$\frac{9+12}{2}\times5=\frac{21}{2}\times5=\frac{105}{2}=52.5$

52.5

Look at the circle in the figure:

The radius is equal to 7.

What is the area of the circle?

Remember that the formula for the area of a circle is

πR²

We replace the data we know:

π7²

π49

49π

Given the rhombus in the drawing:

What is the area?

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:

$\frac{7\times4}{2}=\frac{28}{2}=14$

14

Question 1

Look at the deltoid in the figure:

What is its area?

Question 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.

Question 3

The trapezoid ABCD is shown below.

AB = 2.5 cm

DC = 4 cm

Height (h) = 6 cm

Calculate the area of the trapezoid.

Question 4

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

Question 5

Calculate the area of the right triangle below:

Look at the deltoid in the figure:

What is its area?

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

$\frac{Diagonal1\times Diagonal2}{2}$

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

(4*7)/2

28/2

14

14

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.

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:

$\frac{8\cdot DB}{2}=32$

We will reduce the 8 and the 2:

$4DB=32$

Divide by 4

$DB=8$

8 cm

The trapezoid ABCD is shown below.

AB = 2.5 cm

DC = 4 cm

Height (h) = 6 cm

Calculate the area of the trapezoid.

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

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

We substitute the given values into the formula:

(2.5+4)*6 =

6.5*6=

39/2 =

19.5

$19\frac{1}{2}$

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

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:

$\frac{CB\times AD}{2}$

$\frac{8\times9}{2}=\frac{72}{2}=36$

36 cm²

Calculate the area of the right triangle below:

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:

$\frac{AB\times BC}{2}=\frac{8\times6}{2}=\frac{48}{2}=24$

24 cm²

Question 1

Given the circle whose diameter is 7 cm

What is your area?

Question 2

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

What is its area?

Question 3

Given the following rectangle:

Find the area of the rectangle.

Question 4

Calculate the area of the following triangle:

Question 5

What is the area of the trapezoid in the figure?

Given the circle whose diameter is 7 cm

What is your area?

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

$\pi r^2$

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:

$r=7:2=3.5$

We replace in the formula

$\pi3.5^2=12.25\pi$

$12.25\pi$ cm².

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

What is its area?

Remember that the formula for the area of a circle is

πR²

We replace the data we know:

π3²

π9

$9\pi$ cm²

Given the following rectangle:

Find the area of the rectangle.

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

$9\times6=54$

54

Calculate the area of the following triangle:

The formula for calculating the area of a triangle is:

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

That is:

$\frac{BC\times AE}{2}$

Now we replace the existing data:

$\frac{4\times5}{2}=\frac{20}{2}=10$

10

What is the area of the trapezoid in the figure?

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

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

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

$22$ cm².