# What is the perimeter of the square

### Chocolate bars and their area

Jana and Tarek like to eat chocolate. Jana prefers a variety that looks like a square from above. The sides are all 12 cm long. The Tarek variety is a 16 cm long and 9 cm wide rectangle when viewed from above.

**How big are the area and perimeter?**

Both areas can be divided into centimeter squares. To find the number of all small squares, you can count them all. Then you have that **Area**. Or you just take the length and width times:

**Square:** $$12*12=144$$

**Rectangle:** $$9*16=144$$

Mathematically exactly with the units of measurement:

**Square:** $$ 12 cm * 12 cm = 144 cm ^ 2 $$

**Rectangle:** $$ 9 cm * 16 cm = 144 cm ^ 2 $$

The measure for the area is always square centimeters, square meters, etc.

A square is also a rectangle.

### Calculate area

You designate the sides of a square with small letters: $$ a $$, $$ b $$, $$ c $$, $$ d $$.

If two or more sides **exactly the same length** you can each **same letter** use.

This is the general formula for the area of rectangles:

$$ A = a * b $$

### Special formula for squares

Because with the square **all** Sides are the same length, you can use this formula for squares:

$$ A = a * a $$

or summarized:

$$ A = a ^ 2 $$

The length a and the width b can be called. But it also works the other way around.

The capital A stands for the English word "area". The F has already been assigned to other formulas.

### Calculate sizes

To the **scope** To find a rectangle or a square, you simply add up all the sides:

**Square:** $$12+12+12+12=48$$

**Rectangle:** $$9+16+9+16=50$$

Or more precisely with the units of measurement:

**Square:** $$ 12 cm + 12 cm + 12 cm + 12 cm = 48 cm $$

**Rectangle:** $$ 9 cm + 16 cm + 9 cm + 16 cm = 50 cm $$

### General formula

The following applies to all quadrilaterals:

$$ u = a + b + c + d $$

Because not all sides of rectangles and squares are of different lengths, you can simplify the formula:

**Rectangle:**

$$ u = a + a + b + b = 2 * a + 2 * b $$

**Square:**

$$ u = a + a + a + a = 4 * a $$

Both chocolates cover an area of $$ 144 $$ $$ cm ^ 2 $$, the circumference of Jana's chocolate is $$ 48 $$ $$ cm $$, and the chocolate from Tarek has a circumference of $$ 50 $$ $$ cm $$.

The measure for the circumference is always centimeters, meters, ... So the normal measure of length.

Scope = sum of all pages

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### Rectangle and square are related

### Finally:

What do square and rectangle have in common, what are the differences between them?

Both have four equal (right) angles of 90 ° each.

The opposite sides are the same length for both.

But

**just**in the case of a square, all four sides are the same length.

A square **is** so a rectangle, and a rectangle **can** be a square.

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