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 $m^2$ 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 $m=>m^2$

1. Square

## Examples with solutions for Area

### 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?

### 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

24 cm²

### Exercise #2

Calculate the area of the following triangle:

### 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:

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

We insert the existing data as shown below:

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

10

### Exercise #3

Given the rhombus in the drawing:

What is the area?

### 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:

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

14

### Exercise #4

Given the following rectangle:

Find the area of the rectangle.

### Step-by-Step Solution

Let's calculate the area of the rectangle by multiplying the length by the width:

$2\times5=10$

10

### Exercise #5

Look at the rectangle ABCD below.

Side AB is 4.5 cm long and side BC is 2 cm long.

What is the area of the rectangle?

### Step-by-Step Solution

We begin by multiplying side AB by side BC

We then substitute the given data and we obtain the following:

$4.5\times2=9$

Hence the area of rectangle ABCD equals 9

9 cm²

### Exercise #6

Given the trapezoid:

What is the area?

### Step-by-Step Solution

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

### Exercise #7

The width of a rectangle is equal to 15 cm and its length is 3 cm.

Calculate the area of the rectangle.

### Step-by-Step Solution

To calculate the area of the rectangle, we multiply the length by the width:

$15\times3=45$

45

### Exercise #8

What is the area of the given triangle?

### 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:

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

### Exercise #9

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

### 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:

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

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

36 cm²

### Exercise #10

The trapezoid ABCD is shown below.

AB = 2.5 cm

DC = 4 cm

Height (h) = 6 cm

Calculate the area of the trapezoid.

### Step-by-Step Solution

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

$19\frac{1}{2}$

### Exercise #11

ABCD is a rectangle.

Given in cm:

AB = 7

BC = 5

Calculate the area of the rectangle.

### Step-by-Step Solution

Let's calculate the area of the rectangle by multiplying the length by the width:

$AB\times BC=7\times5=35$

35

### Exercise #12

Calculate the area of the following triangle:

### Step-by-Step Solution

The formula for the area of a triangle is

$A = \frac{h\cdot base}{2}$

Let's insert the available data into the formula:

(7*6)/2 =

42/2 =

21

21

### Exercise #13

Look at rectangle ABCD below.

Side AB is 10 cm long and side BC is 2.5 cm long.

What is the area of the rectangle?

### Step-by-Step Solution

Let's multiply side AB by side BC

We'll substitute the known data and get:

$10\times2.5=25$

The area of rectangle ABCD equals 25

25 cm²

### Exercise #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.

### 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 the product by 2.

We substitute the known data into the formula:

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

We reduce the 8 and the 2:

$4DB=32$

Divide by 4

$DB=8$

8 cm

### Exercise #15

Look at the rectangle ABCD below.

Given in cm:

AB = 10

BC = 5

Calculate the area of the rectangle.

### Step-by-Step Solution

Let's calculate the area of the rectangle by multiplying the length by the width:

$AB\times BC=10\times5=50$