A parallelogram is a quadrilateral with two pairs of opposite sides parallel. It looks like a rectangle that has been pushed over.
You may recall that we can find the area of a rectangle using the formula $\text{Area }=\text{length }\times\text{width }$Area =length ×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. Can you work out why? Think of what each shape has in common and how they differ.
Parallelograms can be easily rearranged into rectangles. In the applet below, we can rearrange a parallelogram with a base $b$b and a perpendicular height $h$h into a rectangle.
The following guide outlines the key features and concepts in the applet.
By using the applet above, we can make the following observations:
The area of a parallelogram is given by
$\text{Area }=\text{base }\times\text{height }$Area =base ×height , or
$A=b\times h$A=b×h
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.
Find the area of the parallelogram below.
Think: This parallelogram has a base of $6$6 cm and a height of $4$4 cm. We can rearrange it into a rectangle with length $6$6 cm and width $4$4 cm.
This rectangle has the same area as the parallelogram, which means we can find the area of the parallelogram by calculating the product of its base and height.
Do: We can use the given dimensions in the formula to find the area.
$\text{Area }$Area | $=$= | $\text{base }\times\text{height }$base ×height | (Formula for the area of a parallelogram) |
$=$= | $6\times4$6×4 | (Substitute the values for the base and height) | |
$=$= | $24$24 | (Perform the multiplication to find the area) |
So the parallelogram has an area of $24$24 cm2.
What is the area of this parallelogram?
Think: The base always refers to a side of the parallelogram, while the height is the perpendicular distance between two opposite sides. In this parallelogram the base is $12$12 m and the height is $17$17 m.
Do: We can use the given dimensions in the formula to find the area.
$\text{Area }$Area | $=$= | $\text{base }\times\text{height }$base ×height | (Formula for the area of a parallelogram) |
$=$= | $12\times19$12×19 | (Substitute the values for the base and height) | |
$=$= | $228$228 | (Perform the multiplication to find the area) |
So the parallelogram has an area of $228$228 m2.
Reflect: Sometimes the height will be labelled within the parallelogram, and sometimes it will be convenient to indicate the height with a label outside the parallelogram.
Complete the table to find the area of the parallelogram shown.
Area | $=$= | base $\times$× height | m2 | |
Area | $=$= | $\editable{}\times\editable{}$× | m2 | (Fill in the values for the base and height) |
Area | $=$= | $\editable{}$ | m2 | (Complete the multiplication to find the area) |
Find the area of the parallelogram shown.
Find the area of a parallelogram whose base is $15$15 cm and height is $7$7 cm.