Finding the Area of Parallelograms and Trapezoids

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SWBAT recognize and use the area formulas for parallelograms and trapezoids.

Big Idea

The Traps of Trapezoids and all things Parallel: Understanding the area of these shapes.

Curriculum Reinforcer

10 minutes

The curriculum reinforcer, is a daily practice piece that is incorporated into almost every lesson to help my students to retain skills and conceptual understanding from earlier lessons. My strategy is to use Spiraled Review to help my students retain what they learned during the earlier part of the year. This will help me to keep mathematical concepts fresh in the students mind so that the knowledge of these concepts become a part of students' long term memories.


10 minutes

In today’s opening exercise, I will provide each of my students with two parallelograms. The parallelograms will be of varying sizes. While passing out the parallelograms, I will ask if there is anyone who knows the formula for the area of a parallelogram. Once I receive the correct answer or provide the correct answer, I will then ask my students, how can the parallelogram be manipulated to create a rectangle. I will provide the students with two minutes to come up with the answer.  Once I receive the correct answer or provide the correct answer, I will then write the formulas for area of both a parallelogram and a rectangle on the board. I will then ask the students if they see any similarities between these two formulas. Once the similarities and differences have been discussed, I will then ask my students to pick up the other parallelogram and see if they can create a trapezoid out of it. Once they have successfully created a trapezoid, I will ask how many trapezoids did they end up creating. Once I receive the desired answer of two, I will write the area formula for a trapezoid on the board and ask my student how does what you have done to the parallelogram compare to this formula.


This exercise as well as the opening from the previous lesson is for the purpose of demonstrating how all of the area formulas that we are dealing with have been derived from the area formula for a rectangle.

Instruction & Teacher Modeling

10 minutes

For today’s instructional piece, I will have my students create an organizer that showcases the properties of special quadrilaterals (squares, rectangles, parallelograms, and trapezoids).

  • What makes them special?
  • What type of quadrilateral is NOT special?
  • What is the difference?
  • What are their formulas?
  • How are their formulas similar/different?

Try It Out

5 minutes

For today’s guided practice, I will demonstrate how to use the formulas for area of parallelograms and trapezoids. I will do this by finding the area of each type of shape mentioned above. I will also show how the ability to use a formula relates to standard EE.2c (evaluate expressions) which is from Unit 3.  

The manner in which I will demonstrate how to use the formulas will be by presenting an example for each type of polygon. One example for the parallelogram and one example for the trapezoid. Please see the attached PowerPoint for the two example problems.

After I demonstrate how to use the formulas, I will then have my students complete two problems of their own.

Independent Exploration

20 minutes

For independent practice, I will have my students practice finding the area of parallelograms and trapezoids. I will give my students 6 word problems, one problem to showcase each type of parallelogram and two trapezoid problems. These word problems will simply present the shapes using their properties.



15 minutes

We will close this lesson by presenting the problems that were completed during the independent practice. To do this, I will select 6 students (one for each of the six problems) to present their work to the rest of the class using the document camera. During the presentation, the students should be able to tell me all of the following:

  • What in the problem lead them to know which shape they were dealing with?
  • What formula did they use?
  • Tell the class step by step how they used the formula to solve the problem?
  • Provide a complete answer to each problem.
  • Provide a visual of the shape and its dimensions.