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: "Parallelogram "
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?