Copy of Area of a Rhombus

Use this worksheet to derive the formula for area of a rhombus. A rhombus is a quadrilateral where all 4 sides are equal. Unlike a square, the angles in each corner are not 90 degrees.[br][br]Use the slider to change the side lengths of the rhombus. Use point C to change the angles.[br]Use the sliders to reflect all four triangles.

1. What shape does the rhombus and the four triangles form?

rhombus square parallelogram rectangle

2. What is the length and width of the new combined shape in terms of [math]d1[/math] and [math]d2[/math]?

Length =2[math]\times[/math][math]d2[/math], width = [math]d1[/math] Length = [math]\frac{1}{2}[/math][math]d2[/math], width = [math]\frac{1}{2}[/math][math]d1[/math] Length =[math]d2[/math], width = 2[math]\times[/math][math]d1[/math] Length = [math]d2[/math], width = [math]d1[/math]

3. Write a formula for the area of the combined figure in terms of [math]d1[/math] and [math]d2[/math].

[math]d1[/math]+[math]d2[/math] 2([math]d1+d2[/math]) [math]2\times d1\times d2[/math] [math]d1[/math][math]\times[/math][math]d2[/math]

4. What fraction of the combined shape was the original rhombus?

[math]\frac{2}{1}[/math] [math]\frac{1}{3}[/math] [math]\frac{1}{2}[/math] [math]\frac{3}{1}[/math]

5. Write a rule for the area of rhombus ABCD in terms of [math]d1[/math] and [math]d2[/math].

[math]\frac{\left(d1\times d2\right)}{2}[/math] [math]d1\times d2[/math] [math]\frac{1}{2}\left(d1\times d2\right)[/math] [math]\frac{1}{2}\left(d1+d2\right)[/math]

Copy of Area of a Rhombus

Information: Copy of Area of a Rhombus