Definition: A rhombus is a parallelogram with 4 congruent sides (equal length).

Interactivity 1 - Rhombus    Directions for interactivity

Click and drag the slider buttons to change the size. Click and drag point B to move and point А to rotate.

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Basic formulas for a rhombus with side a and height h: perimeter is: L=4a , and area is: A=ah .

Examples with perimeter and areas of rhombi

Check the following examples using the above interactivity.

a h Perimeter: L=4a Area: A=ah
3 \,cm 4 \,cm 4\cdot 3 = 12\,cm 3 \, cm \cdot 4 \,cm=12 \,cm^2
2,5 \, m 4 \,m 4 \cdot 2,5 \,m=10 \,m 2,5 \,m \cdot 4 \,m=10 \,m^2
0,07 \,m 60 \,mm 4 \cdot 7 \,cm =28 \,cm 7 \,cm \cdot 6 \,cm=42 \,cm^2
0,07 \,m 60 \,mm 4 \cdot 0,07 \,m =2,8 \times 10^{-1} \,m 0,07 \,m \cdot 0,06 \,m=4,2 \times 10^{-3} \,m^2

Interactivity 2: Construct a rhombus

1. Examine the rhombus in the above interactivity..

2. Now construct a rhombus with the same properties. If you need help with the steps, click here to open a new window with directions?.

Check whether your construction is stable - Is your construction always a rhombus no matter what slider or point you move?
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Еquivalent definitions:
  • A rhombus is a parallelogram whose diagonals intersect at a right angle.

Theorems

  • A rhombus is completely determined by the length of a side a and the height h \,\,( \text{sin} \alpha = \frac{h}{a} ).
  • A rhombus is completely determined by the length of a side a an an angle \alpha \,\, ( h=a \, \text{sin} \alpha ).
  • The diagonals of a rhombus bisect themselves(a rhombus is a parallelogram).

The diagonals of a rhombus intersect at a right angle.   Interactivity

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Page last modified on March 09, 2008, at 10:21 AM