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Area of a Trapezoid

Author:Mikki Becker, Duane Habecker, Tim Brzezinski
In the box below, the trapezoid should have a base 1 () of 2 units, a base 2 () of 6 units, and a height (h) of 3. If it does not, move the blue vertices to create a trapezoid with those dimensions. Then, slide the slider.

The slider took a copy of the original trapezoid, flipped it, and connected it to the original trapezoid. What shape do the two trapezoids make?

Select all that apply
  • A
  • B
  • C
  • D
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How many units is the base of the new shape?

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How many units is the height of the new shape?

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What is the area of the new shape?

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You found the area of the new shape, which is made up of two identical trapezoids. What is the area of one of the trapezoids?

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Great work! You found the area of a trapezoid! Let's make a new one and try it again. Move the blue vertices to create a trapezoid where , , and . Once you have made the trapezoid with the given dimensions, slide the slider.

What is the base of the parallelogram?

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What is the height of the parallelogram?

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What is the area of the parallelogram?

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What is the area of the trapezoid?

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Nice! Let's try another one. Move the blue vertices to create a trapezoid where , , and . Once you have made the trapezoid with the given dimensions, slide the slider.

What is the area of the parallelogram?

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What is the area of the trapezoid?

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Superb! Let's try another one. Move the blue vertices to create a trapezoid where , , and . Once you have made the trapezoid with the given dimensions, slide the slider.

What is the area of the parallelogram?

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What is the area of the trapezoid?

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Amazing! Let's try one more. Move the blue vertices to create a trapezoid where , , and . Once you have made the trapezoid with the given dimensions, slide the slider.

What is the area of the trapezoid?

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Now that you've had some practice, describe the steps it takes to find the area of a trapezoid.

Challenge:

What is the greatest area you can make with a right trapezoid (a trapezoid with two right angles) that has a perimeter of 46 units?

Move the LARGE POINTS to create different trapezoids with fixed perimeter = 46 units. If the trapezoid disappears, make it smaller so it reappears.

What maximum possible area did you find? What were the dimensions of this trapezoid?

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