A parallelogram is a quadrilateral with two pairs of opposite sides parallel. A rectangle is a special type of parallelogram but parallelograms do not have to have right angles. Both shapes below are examples of parallelograms.
You may recall that we can find the area of a rectangle using the formula \text{Area}=\text{length}\times\text{width}, and we will see that finding the area of a parallelogram is very similar. We will make use of the base and perpendicular height of the parallelogram to find its area.
Notice that a rectangle is a type of parallelogram, but not all parallelograms are rectangles. Why might this be? Think of what each shape has in common and how they differ.
Parallelograms can be easily rearranged into rectangles. Explore this using the applet below.
After using the applet above, we can make the following observations:
The area of a parallelogram is given by
\begin{aligned} \text{Area}&=\text{base}\times\text{height}\\ A&=b\times h \end{aligned}
Unlike a rectangle, there are generally no right angles in a parallelogram. But we should remember that the height and base are at right angles to each other when we work out the area of a parallelogram.
Consider the following parallelogram.
If the parallelogram is formed into a rectangle, what would the length and width of the rectangle be?
Find the area of the parallelogram.
Find the area of a parallelogram whose base is 15\text{ cm} and height is 7\text{ cm}.
The area of a parallelogram is given by: