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

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

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

$a$ –> 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

$r$   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

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.

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.