Geometric shapes on the Plane_3  
Section: Geometry  
1. THE AREA OF A RHOMBUS (1st WAY)  
The
rhombus is a special kind of parallelogram with four equal sides. If
we know the base and height we can use the formula for working out the
area of a parallelogram. However, the area of a rhombus is often
expressed by referring to its diagonal lines. The
area of a rhombus, in terms of its diagonals is:
In the shape below you can see that we have called the diagonals a and b. We have also drawn a rectangle around the rhombus as we are going to use the rectangle to help us work out the area of a rhombus. 

1. Click on the button and four green triangles should appear which are the same as the four triangles that make up the rhombus. 2. Therefore we can say that the area of a rhombus is half of the area of a rectangle.

2. THE AREA OF A RHOMBUS ( 2nd WAY )  
In the following window we can see how a different construction can be used to work out the area of a rhombus. 

1. Follow all the steps indicated by the window and then try to explain how this demonstration works to find out the area. 2. Go back to the area of a triangle page and review the window where we constructed different triangles with the same area. This will help you to understand step 3. 
Agustín Muñoz Núñez  
Spanish Ministry of Education. Year 2001  
Except where otherwise noted, this work is licensed under a Creative Common License