Copy of Area of a Trapezoid

Use this dynamic worksheet to derive the formula for area of a trapezoid.

Use the slider to rotate the trapezoid around BD.[br][br]

1. What shape do the two combined trapezoids form?

trapezium kite parallelogram rectangle

2. Let b1 represent the length of AB and b2 represent the length of CD.[br]What is the length of the base of the shape formed by the combined trapeziums?

b1 X b2 b1+b2 b1 b2

3. Write the formula for the combined shape in terms of b1, b2 and h.

[math]\left(b1+b2\right)\times h[/math] [math]b1\times b2\times h[/math] [math]\frac{\left(b1+b2\right)}{h}[/math] [math]b1+b2+h[/math]

What fraction of the combined shape is the original trapezium?

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

Write a rule for the area of the original trapezium in terms of b1, b2 and h.

[math]\frac{1}{2}\left(b1+b2\right)h[/math] [math]2\left(b1+b2\right)h[/math] [math]\frac{\left(b1+b2\right)}{h}[/math] [math]\frac{\left(b1+b2\right)h}{2}[/math]

Copy of Area of a Trapezoid

What fraction of the combined shape is the original trapezium?

Information: Copy of Area of a Trapezoid