Area of Triangles 1
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How to find areas of triangles using the formula: A = ½base×height.

This topic is part of the TCS FREE high school mathematics 'How-to Library', and will help you to find areas of triangles using the formula: A = ½base×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.


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

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

For a right angled triangle, the perpendicular height can be one of the sides:

For an obtuse angled triangle (that is, a triangle with an angle greater than 90°) the perpendicular height may lie outside of the triangle itself:

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

Area  =  ½ × base × perpendicular height


Maths Helper Plus can show the calculations and also draw a diagram for calculating the area of a triangle 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:  'Triangle Area 1.mhp'   File size: 7kb
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 triangle. 

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

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


Step 3  Adjust the shape of the triangle diagram

NOTE: The following procedure does not effect the calculations in any way because the base and perpendicular height remain the same.

If you know the shape of the triangle (eg if you have been given a diagram) then you can adjust the shape of the triangle in Maths Helper Plus to look like your triangle. 


The 'C' value in the parameters box is the distance of the top vertex of the triangle from the left side of the base. For example...


C between zero and B:

C equal to zero:
C less than zero:


Step 4  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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