## How to Calculate the Area of a Parallelogram

A parallelogram is a quadrilateral (polygon with 4 sides) whose opposite sides are parallel.

Below are some of the examples of a parallelogram. As you can see, squares and rectangles are parallelograms because their opposite sides are parallel. They are the parallelograms with right angles. The third quadrilateral below is a parallelogram with no right angles.

In this post, we are going to discuss how to calculate the area of a parallelogram. Since we have already discussed how to calculate the **areas of squares **and** rectangles**, we will focus on areas of non-right angled parallelograms such as the third figure above.

Consider parallelogram *ABCD* in the next figure. Side *AD* is the *base* and the blue dashed line the *height*. Using them, how do we calculate the area of *ABCD*?

Notice that if we drop a line (a height) from *C* and extend *AD* to the right (see next figure), then we can form triangle *DCF*. This triangle has the same size and shape as triangle *ABE. *This is because of the SAS Congruence — if you want to study further.

Now since the triangles have the same size and shape, this means that I can place *ABE* to exactly cover *DCF* making it a rectangle as shown below. Now, we find the area of rectangle *BCFE* which is equal to the area of the original parallelogram (can you see why?).

We know that the area of a rectangle is the product of its length and width. In the previous figure, the length of the rectangle is *BC*. But we know that *BC* is the opposite side of *AD* in the original figure and opposite sides of a parallelogram are also of the same length, so *BC* has the same length as the base of the original figure.

The width of the rectangle is *CF* which is equal to the height of the parallelogram. So, the area of a parallelogram is the product of the length (the base of the original figure) and the width (the height of the parallelogram).

Therefore,

**Area = base x height.**

In the **next post**, we will have some sample problems regarding area of parallelogram.