## Area Tutorial 3 – Area of a Parallelogram

In the previous area computation tutorials, we have learned how to compute the area of a rectangle and the area of a triangle. In this tutorial, we are going to learn how to compute the area of a parallelogram.

In *Figure 1*, we have parallelogram ** ABCD** with given base and the dashed segment as its height. If we drop down a vertical segment from point

**and extend a horizontal segment from**

*C***to the right, we can form triangle**

*D***as shown in**

*CDF**Figure 2*.

Now, angle ** ABE** is congruent to angle

**(Why?),**

*DCF***is congruent to**

*AB***, and angle**

*CD***is congruent to angle**

*BAE***Hence, by**

*CDF*.**congruence postulate, triangle**

*ASA***is congruent to triangle**

*ABE***.**

*DCF*Since triangle ** BAE** is congruent to triangle

**, we can move**

*CDF***to coincide with**

*ABE***forming the rectangle in**

*DCF**Figure 3*. Click here to explore the translation using GeoGebra.

Since ** BCFE** is a rectangle, its area therefore is the product of its base (length) and its height (width). We removed nothing from the parallelogram, therefore, the area of the parallelogram is the same as that of the area of the rectangle. Thus, the area of a parallelogram is the product of its base and its height.

Mr. Pilarski has almost a similar explanation but in video format.

**Enjoy and Learn More**