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Area of Parallelograms


Not quite a rectangle!

A parallelogram is similar to a rectangle, but it has no right angles, so it's not quite a rectangle.


What about area?

The good news is, we can use the similarities between parallelograms to help calculate the area of a parallelogram. Take a look at how this is possible, and then use the applet to turn a parallelogram into a rectangle, and vice-versa.

Did you know?

A rectangle is a parallelogram, but a parallelogram is not a rectangle. Can you work out why? Think of what they have in common, and how they differ.


The rule

Because a parallelogram might not have right angles, we need to make sure we use the perpendicular height, when we work out the area. The video shows you what that means, and what to look out for.



It doesn't matter which side you use as the base, as long as the height is the perpendicular height. 


Back to where we started

If we use the base and perpendicular height (the dimensions) of our parallelogram to work out its area, we can use the area and one of the dimensions, to work out the missing one. Remember that Area = base × height (or, $A=bh$A=bh), so we can use division to work backwards. Take a look:


Change the shape

Here's a chance to change the base and perpendicular height of a parallelogram, and see how the area changes.  Play around with the sliders to change the dimensions and area, and work out the missing value.


The real world

If you come across a problem where you need to calculate the area of a parallelogram, you only have to remember the rule for its area, or how to work out the dimensions of a parallelogram from its area. Then, you can solve the problem as you would for any other shape. 


Practice questions

Question 1

Find the area of the parallelogram shown.


A parallelogram is shown. The base measures 21cm. The height measures 20 cm, as represented by a vertical dashed line inside the parallelogram which is drawn perpendicularly from the top side to the bottom right vertex.

Question 2

Find the unknown measure in the parallelogram pictured, given that its area is $255$255 square units.

Question 3

Some car parks require the cars to park at an angle as shown.

The dimensions of the car park are as given, where each individual parking space has a length of $4.9$4.9 m and a width of $4.4$4.4 m.

What area is needed to create an angled carpark suitable for $7$7 cars?

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