Area of a Triangle

You already know how to find the area of a parallogram. Now we will consider the area of a triangle.

The diagram on the right shows the base and height of a triangle. The height is the length of a perpenticular line from a vertex to the opposite side (the distance from the vertex to the side).

Take any triangle and an exact copy of it, put these two together, you will get a parallelogram of the same height and base. This is the key to finding the area of a triangle.

1. A triangle is shown in the following diagram. You can drag the points to change the triangle.

2. In the above diagram,

   1. Click "Copy the Triangle ABC" to make an exact copy of it.

   2. Move and rotate the copy to join with the original tirangle to form one figure with four sides (a quadrilateral). Click the button "Join" to merge the two triangles into a quadrilateral.

   3. There are two different ways to to form the quadrilateral with the same height h. Use the buttons "join" and "join the other way" to find out.

3. Based on the experiments in the previous step, answer these questons.

   • The quadrilateral you formed have twice the area as the triangle ABC.        

   • Is the quadrilateral you formed this way a parallelogram?        

   • Given a parallelogram with height h= and base b= , compute its area.
     Area =

4. After performing the above steps, it is time to

Exploration

Try the enclosing-rectangle approach.

Try to verify that the quadrilateral is actually a parallelogram.

Comprehension Assessment

Test yourself to see if you have fully absorbed this lesson.

Related Topics

Intro to area, area units, rectangle, parallelogram, angles, parallel lines.

Teacher/Study Guide

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