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 $m=>m^2$

AB = 10 cm

The height of the rectangle is 5 cm.

Calculate the area of the parallelogram.

**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

AB = 12 cm

The height of the rectangle is 4 cm.

Calculate the area of the parallelogram.

Question 2

AB = 15 cm

The height of the rectangle is 6 cm.

Calculate the area of the parallelogram.

Question 3

AB = 17 cm

The height of the rectangle is 8 cm.

Calculate the area of the parallelogram.

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

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

AB = 25 cm

The height of the rectangle is 13 cm.

Calculate the area of the parallelogram.

Question 2

AB = 32 cm

The height of the rectangle is 15 cm.

Calculate the area of the parallelogram.

Question 3

AB = 3 cm

Height of the rectangle = 1.5 cm

Calculate the area of the parallelogram.

$a$ –> 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

AB = 5 cm

The height of the rectangle is 2 cm.

Calculate the area of the parallelogram.

Question 2

AB = 6 cm

The height of the rectangle is 2 cm.

Calculate the area of the parallelogram.

Question 3

AB = 7 cm

Height of the rectangle = 3.5 cm

Calculate the area of the parallelogram.

$r$ 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

ABCD is a parallelogram.

AH is the height.

DC = 6

AH = 3

What is the area of the parallelogram?

Question 2

ABCD is a parallelogram.

AH is its height.

Given in cm:

AB = 7

AH = 2

Calculate the area of the parallelogram.

Question 3

ABCD is a rectangle.

Given in cm:

AB = 7

BC = 5

Calculate the area of the rectangle.

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

ABDC is a deltoid.

AB = BD

DC = CA

Given in cm:

AD = 12

CB = 16

Calculate the area of the deltoid.

Question 2

ACBD is a deltoid.

AD = AB

CA = CB

Given in cm:

AB = 6

CD = 10

Calculate the area of the deltoid.

Question 3

AB = 10 cm

The height of the rectangle is 5 cm.

Calculate the area of the parallelogram.

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.

ABCD is a rectangle.

Given in cm:

AB = 7

BC = 5

Calculate the area of the rectangle.

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

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

35

ABDC is a deltoid.

AB = BD

DC = CA

Given in cm:

AD = 12

CB = 16

Calculate the area of the deltoid.

First, let's recall the formula for the area of a rhombus -

(Diagonal 1 * Diagonal 2) divided by 2

Let's substitute the known data into the formula:

(12*16)/2

192/2=

96

And that's the solution!

96 cm²

ACBD is a deltoid.

AD = AB

CA = CB

Given in cm:

AB = 6

CD = 10

Calculate the area of the deltoid.

To solve the exercise, we first need to remember how to calculate the area of a rhombus:

(diagonal * diagonal) divided by 2

Let's plug in the data we have from the question

10*6=60

60/2=30

And that's the solution!

30

Calculate the area of the following parallelogram:

To solve the exercise, we need to remember the formula for the area of a parallelogram:

Side * Height perpendicular to the side

We can identify that in the diagram, although it's not presented in the way we're familiar with, we are given the two essential pieces of information -

Side = 6

Height = 5

Let's substitute into the formula and calculate:

6*5=30

And that's the solution!

30 cm²

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:

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

We insert the existing data as shown below:

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

10

Do you know what the answer is?

Question 1

AB = 12 cm

The height of the rectangle is 4 cm.

Calculate the area of the parallelogram.

Question 2

AB = 15 cm

The height of the rectangle is 6 cm.

Calculate the area of the parallelogram.

Question 3

AB = 17 cm

The height of the rectangle is 8 cm.

Calculate the area of the parallelogram.

Related Subjects

- Area
- Trapezoids
- Symmetry in Trapezoids
- Diagonals of an isosceles trapezoid
- Area of a trapezoid
- Perimeter of a trapezoid
- Types of Trapezoids
- Isosceles Trapezoid
- Parallelogram
- The area of a parallelogram: what is it and how is it calculated?
- Perimeter of a Parallelogram
- Identifying a Parallelogram
- Rotational Symmetry in Parallelograms
- From the Quadrilateral to the Parallelogram
- Kite
- Area of a Deltoid (Kite)
- Congruent Triangles
- Parallel lines
- Angles In Parallel Lines
- Alternate angles
- Corresponding angles
- Collateral angles
- Vertically Opposite Angles
- Adjacent angles
- The Pythagorean Theorem
- Elements of the circumference
- Circle
- Diameter
- Pi
- Area of a circle
- Distance from a chord to the center of a circle
- Chords of a Circle
- Central Angle in a Circle
- Arcs in a Circle
- Perpendicular to a chord from the center of a circle
- Inscribed angle in a circle
- Tangent to a circle
- The Circumference of a Circle
- The Center of a Circle
- Radius
- How is the radius calculated using its circumference?
- Rectangle
- From a Quadrilateral to a Rectangle
- From a Parallelogram to a Rectangle
- Calculating the Area of a Rectangle
- The perimeter of the rectangle
- Congruent Rectangles
- The sides or edges of a triangle
- Similarity of Triangles and Polygons
- Triangle similarity criteria
- Triangle Height
- Midsegment
- Midsegment of a triangle
- Midsegment of a trapezoid
- The Sum of the Interior Angles of a Triangle
- Exterior angles of a triangle
- Relationships Between Angles and Sides of the Triangle
- Relations Between The Sides of a Triangle
- Square
- Area of a square
- From Parallelogram to Square
- Rhombus, kite, or diamond?
- Diagonals of a Rhombus
- Lines of Symmetry in a Rhombus
- From Parallelogram to Rhombus
- The Area of a Rhombus
- Perimeter
- Triangle
- Types of Triangles
- Obtuse Triangle
- Equilateral triangle
- Identification of an Isosceles Triangle
- Scalene triangle
- Acute triangle
- Isosceles triangle
- The Area of a Triangle
- Area of a right triangle
- Area of Isosceles Triangles
- Area of a Scalene Triangle
- Area of Equilateral Triangles
- Perimeter of a triangle
- Cylinder Area
- Cylinder Volume
- Cuboids
- Cubes
- How to calculate the surface area of a rectangular prism (orthohedron)
- How to calculate the volume of a rectangular prism (orthohedron)
- Lateral surface area of a rectangular prism
- Right Triangular Prism
- Bases of the Right Triangular Prism
- The lateral faces of the prism
- Lateral Edges of a Prism
- Height of a Prism
- The volume of the prism
- Surface area of triangular prisms