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Copy of Area of a Trapezoid

Let's Derive the Area of a Trapezoid!

The formula for the area of a trapezoid is . There are a few different ways we can prove this.

Deriving the formula using a parallelogram:

What is the area formula of a parallelogram?

How can we write the area of the parallelogram in terms of the original trapezoid from the graph above?

*Note: when you move the top half of the trapezoid, the label for side a moves. However, a is still the line segment AB

Deriving the formula using a rectangle and a triangle:

We can find the area of the trapezoid by adding the areas of the rectangle and the triangle it is made up of.

What is the area formula of a rectangle?

What is the area formula of a triangle?

What variable represents the base of the rectangle? *Hint: Think about how we split the trapezoid up. If you're not sure, take a look at the graph below.

What expression represents the base of the triangle? *Look at the graph

If the base of the trapezoid is b and we removed a, the base of the triangle would be (b - a)

Now, try adding the formulas for the area of the rectangle and the triangle in terms of a, b, and h. See if it matches the area of a trapezoid.