# What is the area of a parallelogram

### From rectangle to parallelogram

### Is there a "crooked" rectangle?

Rectangles whose sides have been flipped might look like this:

Of course, these are no longer rectangles, but **Parallelograms**. And the "crooked" square becomes **Rhombus** called.

The same applies here as with the rectangle: If two or more sides **exactly the same** are long, you use **same** Letters.

The **opposite** Pages are **parallel**. Therefore the name: "**Parallel**ogram "

The diamond is also called the rhombus.

### Calculate the scope

The **scope** You calculate the parallelogram in the same way as for the rectangle.

### General formula

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

Because the opposite sides each **of equal length** you can simplify the formula:

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

You can use the same general formula to calculate the circumference for all of the squares.

Scope = sum of all pages

### Calculate area

With the area it is not as easy as with the rectangle. You cannot use the formula $$ A = a * b $$ here because the sides are crooked.

### But there is a trick:

Cut off a triangle on the left and move it to the right.

So you get a **rectangle**, the **same** Has area like that **parallelogram**.

The **new page** is the **Height h**. It is the height of the rectangle and the parallelogram.

The formula for the area is then:

$$ A = a * h $$

You can also write exactly:

$$ A = a * h_a $$

$$ h_a $$ is the height to the $$ a $$ side.

**Page A** also known as **Base side** of the parallelogram. Sometimes she is therefore with **G** named.

Then the formula is:

$$ A = g * h $$

If you want to calculate the area, the sides must be perpendicular to each other.

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

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### Now is the time to calculate

### Example:

How big are the circumference and area of the parallelogram?

**Scope:**

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

$$ u = 2 * 16 + 2 * 12 = 56 $$

More precisely with the units of measurement:

$$ u = 2 * 16 $$ $$ cm + 2 * 12 $$ $$ cm = 56 $$ $$ cm $$

**Area:**

$$ A = a * h $$

$$ A = 16 * 9 = 144 $$

More precisely with the units of measurement:

$$ A = 16 $$ $$ cm * 9 $$ $$ cm = 144 $$ $$ cm ^ 2 $$

The circumference is $$ 56 $$ $$ cm $$.

The parallelogram is $$ 144 $$ $$ cm ^ 2 $$ large.

**Important:** The height h is perpendicular to the side a.

Area = length (base side) times height

### Rectangle and parallelogram are related

### Finally: What do rectangles and parallelograms have in common, what are the differences between them?

- Both sides have the same length on opposite sides.
- The diagonally opposite angles are the same for both.
- But only with the rectangle are all four angles the same (each with 90 °).

So a rectangle is also a parallelogram and a parallelogram **can** be a rectangle.

##### When is a rectangle not a parallelogram?

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