Area of a parallelogram

The area of a parallelogram is the size of the region that the parallelogram covers. A parallelogram is a shape similar to a rectangle, but with two opposite sides slanted, as in the picture.

Let the lengths of the two different sides be a and b. We also need the height h perpendicular to side a. Given the height h, the area of the parallelogram, which we denote S, is

$$S=a\cdot h$$

The parallelogram above has side a = 4 and height h = 2, so its area is

$$S=4\cdot 2=8$$

Why is the formula the same as for the area of a rectangle? Because we can take the triangle that sticks out on the left-hand side and move it to the right-hand side, where something is missing. The area does not change, but now we have a rectangle, so we can use the formula we already know.

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