Area of Parallelograms
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How to find areas of parallelograms using the formula: A = base×height.

This topic is part of the TCS FREE high school mathematics 'How-to Library', and will help you to find areas of parallelograms using the formula: A = base×height.
(See the index page for a list of all available topics in the library.) To make best use of this topic, you need to download the Maths Helper Plus software. Click here for instructions.

Theory:

The base and perpendicular height of a parallelogram can be identified as follows:

Any side can be the base, and then the perpendicular height extends from the side parallel to the base to meet a line through the base at a 90° angle.

For a rectangle, the perpendicular height is one of the sides:

If you know the base and perpendicular height of a parallelogram, then you can find the area using this formula:

Area  =  base × perpendicular height

Method:

Maths Helper Plus can show the calculations and also draw a diagram for calculating the area of a parallelogram given the base and perpendicular height.  

Step 1 Download the free support file... We have created a Maths Helper Plus document to complement this topic. You can use it to practice the steps described below, and as a starting point for solving your own problems.

File name:  'Area of Parallelogram.mhp'   File size: 10kb
Click here to download the file.

If you choose 'Open this file from its current location', then Maths Helper Plus should open the document immediately. If not, try the other option: 'Save this file to disk', then run Maths Helper Plus and choose the 'Open' command from the 'File' menu. Locate the saved file and open it. If you do not yet have Maths Helper Plus installed on your computer, click here for instructions.

Step 2  Display the parameters box

Press the F5 key to display the parameters box:

 

Click on the 'A' edit box with the mouse, then type the perpendicular height of your parallelogram. 

Similarly, click on the 'B' edit box and type the value of the base. 

 

The 'C' value is the length of the vertically slanted sides of the parallelogram. For a rectangle, make 'C' equal to 'A'. For a more slanted parallelogram, make 'C' a larger value.

NOTE: The diagram will not display if 'C' is greater than 'B'.

 

Click the 'Update' button to refresh the diagram and calculations.

 

Step 3  Adjust the scale of the labelled diagram

If the labelled diagram does not display the points, the scale needs to be reduced. In this case, briefly press the F10 key enough times until the two plotted points are seen.

 

You can make the diagram bigger by holding down 'Ctrl' while you press F10.

 

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