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 $m=>m^2$

A circle has a diameter of 4 cm.

What is its area?

**Now we will learn to calculate the area of (almost) all the shapes we know! Are we ready?**

$a$ Side of the square

$a\times a=Area~ of ~the ~square$

$A=a^2$

We will multiply the side of the square by itself

**Another way:**

$\frac{diagonal \times diagonal}{2}=Area~ of ~the ~square$

For more information, enter the link of **Area of a square**

Test your knowledge

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

The center of the circle in the diagram is O.

What is the area of the circle?

$a\times b=Area~of~the~rectangle$

We will multiply one side of the rectangle by the adjacent side (the side with which it forms a $90^o$ degree angle)

For more information, enter the link of **Rectangle area**

$\frac{height~\times corresponding~side}{2}=Area~ of ~the ~triangle$

We will multiply the height by the corresponding side - that is, the side with which it forms a $90^o$ degree angle and divide the product by $2$.

For more information, enter the link to **Triangle Area**

Do you know what the answer is?

Question 1

Look at the circle in the figure:

The radius is equal to 7.

What is the area of the circle?

Question 2

Look at the circle in the figure:

\( \)

The radius of the circle is 4.

What is its area?

Question 3

O is the center point of the circle below.

Is it possible to calculate its area?

$a$ –> Side of the rhombus

$h$ –> Height

$a\times h= Area~ of ~the~ rhombus$

We will multiply the height by the corresponding side, that is, the side with which it forms a right angle of $90^o$ degrees.

**Another way :**

$\frac{diagonal\times diagonal}{2}=Area~ of~ the~ rhombus$

For more information, enter the link of **Rhombus area**

$H$ –> Height

$B$ –> The side that forms a $90^o$ degree angle with the height $H$.

We will multiply the height by the side to which the height reaches and forms with it a $90^o$ degree angle.

$B\times H=Area~ of ~the~ parallelogram$

For more information, enter the link of **Parallelogram area**

Check your understanding

Question 1

Look at the circle in the diagram.

AB is a chord.

Is it possible to calculate the area of the circle?

Question 2

A circle has an area of 25 cm².

What is its radius?

Question 3

Look at the circle in the figure:

The diameter of the circle is 13.

What is its area?

$r$ The radius of the circumference

$π$ PI

It will be calculated as the number $3.14$

$π\times r^2=Area~ of ~the ~circle$

We will multiply PI $3.14$ by the radius of the circumference squared, that is $r^2$** Or, more simply, the formula is:**

$r\times r\times 3.14=Area~ of ~the ~circle$

For more information, enter the link of **Circle area**

We will add the bases and multiply the result by the height of the trapezoid.

We will divide the result by $2$.

$\frac{(a+b)\times h}{2}=Area~ of~ the~ trapezoid$

For more information, enter the link of **Trapezoid area**

Do you think you will be able to solve it?

Question 1

A pizza has a diameter of 45 cm. It is cut into eight slices. What is the area of each slice?

Question 2

Look at the circle in the figure.

What is the diameter of the circle?

Question 3

Look at the circle in the figure below.

What is the radius of the circle?

We will multiply the diagonals and divide by $2$.

$\frac{ac\times db}{2}=Area~ of~ the~ trapezoid$

For more information, enter the link of **Area of the kite**

You don't have to worry about this pair of terms - composite figures. They are not called composite because they are complicated or difficult, but rather, they are composite figures because they are really made up of several figures that you already know.

The great key to calculating the area of this type of figures is to separate them into several simple figures on which you know how to calculate their area.

At first glance, it might scare us a bit since the figure seems very strange. But, very quickly we will remember the suggestion that we have written here above and apply it.

We will realize that we can divide the composite figure into two that we know and know how to calculate their area, rectangle and square.

We will calculate the area of each figure separately and then add them together.

In this way, we will obtain the area of the entire figure.

Test your knowledge

Question 1

Given the semicircle:

What is the area?

Question 2

Pacman's radius 6 cm.

The angle of Pacman's mouth is 45 degrees.

What is Pacman's area?

Question 3

A circle has a diameter of 4 cm.

What is its area?

To understand the difference, let's remember a daily term we use in another context: superficial.

Superficial implies something or someone without depth, so, in geometry, the surface indicates the size of something flat, without depth. For example, if we draw a ball and paint it, that painted part would be its surface.

On the other hand, volume refers to the actual size of the ball, the space that we could fill inside it.

Volume is not the surface on the sheet of paper, but, really the size we can see (in a three-dimensional way) - the space it occupies in space.

The calculation of volume differs from the calculation of the surface.

Do you know what the answer is?

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

The center of the circle in the diagram is O.

What is the area of the circle?

Related Subjects

- Area of Equilateral Triangles
- Area of a Scalene Triangle
- Area of Isosceles Triangles
- Area of a right triangle
- Trapezoids
- Parallelogram
- Perimeter of a Parallelogram
- How is the radius calculated using its circumference?
- Tangent to a circle
- The Center of a Circle
- Area of a circle
- Inscribed angle in a circle
- Central Angle in a Circle
- Cylinder Volume
- Perimeter
- Triangle