Rhombus
Areas of plane figures
 

Deduce the formula for the area of a rhombus, knowing its diagonals.

The rhombus is a parallelogram and so, to find its area, we can multiply its base by its perpendicular height.
However, if we know its diagonals insread of its base and height, we can use another formula. You have to deduce that formula.

 

Drag the rhombus to the right. An uncoloured rhombus divided into four rectangles will appear underneath.

Take each of these triangles next to the rhombus in such a way that all together, they form a rectangle. 

- What is the relation between the resulting rectangle and the rhombus?

- What are the measurement of  the  diagonals of the rhombus equivalent in the rectangle?

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What is the relation between the area of the rhombus and the rectangle area?

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With this information, deduce the formula for the area of the rhombus knowing its diagonals. Write it down in your notebook.


       
           
  Eduardo Barbero Corral
 
Spanish Ministry of Education , Social Afairs and Sport. Year 2007
 
 

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