Finding the Area of Composite Plane Figures

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SWBAT demonstrate that they can decompose irregular plane figures into regular plane figures and use their knowledge of regular plane figures to solve the areas of irregular plane figures.

Big Idea

Area 51 Ain’t Got Nothin’ On These Areas! The composition of composite figures

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 present to my students a picture of an irregular shaped polygon. The students will be asked to decompose the figure into the least amount of regular plane figures possible. I will present this as a challenge to my students.

Afterward my students have decomposed the plane composite figure into regular plane figures, I will then have them draw the plane figures and, I will then challenge the students to find the measurements of as many sides of the regular plane figures as they are able.

I will then choose two students to show how they decomposed their polygon and demonstrate how they found the measurements of the different sides of the regular plane figures within the composite figure.

These students will be chosen purposefully, as I will be traveling the room to see what they were able to figure out. I will also be answering questions and gauging the level of understanding as I observe my students' work.

Instruction & Teacher Modeling

10 minutes

In this lesson, I will be introducing the students to methods to finding the area of composite figures. I will do this by first demonstrating how they can use what they have done during the opening exercise to find the total area of the polygon presented to them. In doing so, I will be placing an emphasis on methods of decomposing irregular polygons into regular polygons whose areas can be found using a formula. I will also be placing emphasis on my students' ability to determine the measurement of the missing sides of the regular shapes. 

Students are already familiar with how to find the area of basic regular polygons. Therefore, this lesson will focus more on how to find and determine the side lengths of the basic regular polygons within a composite figure for the purpose of finding the total area of a composite figure.

To model this for my students, I will use the opening exercise and show students how to find the total area of the composite figure that was presented to them during that portion of the lesson. They will use the side lengths that they already found to determine the total area of the figure.


Try It Out

10 minutes

For today’s guided practice, we will practice finding the area of three types of composite plane figures. I will present my students with the PowerPoint attached to this section of this lesson. And, I will allow them approximately 5 minutes to work on the problems while I travel the room answering questions and clearing up misconceptions.

Then, I will spend another 5 minutes demonstrating to students how they should have gone about finding the area of these figures. At this time, the students should be comparing their solutions to mine to see where they made mistakes, they should be taking notes and changing whatever is necessary to change to make their solutions correct. The reason for this is to ensure that they have notes that they can later look at to help them when completing homework or other independent work.

Independent Exploration

20 minutes

After completing the, "Try It Out" section of this lesson, my students should have enough information to help them get through today’s independent practice. The independent practice for today’s lesson requires the student to estimate the area of two non-polygons and find the area of four irregular polygons.

I will present the 4 irregular polygons to my students first. This is the portion of the assignment that is for all students. Then, as those students of mine who are higher achievers finish, I will then present them with the two non-polygon composite figures. This is a challenge strictly for my higher achieving students, however, I will not keep any student who wants to give it a try from attempting the problems. 

As the students are working, I will pull a small group to help. These students will consist of those who I observed struggling during the "Try It Out" portion of this lesson. As I am working with the struggling students, the rest of the students may use each other as a resource and support. However, they may only ask questions and collaborate with students at their table. Should any of them need more than what a peer can provide them, then they may raise their hand to get permission to interrupt the group.

Closing Summary

10 minutes

To close out the lesson, I will choose one student per problem to present their solutions under the document camera. The chosen students will have to explain step by step what they did in order to solve for the area of the given figure. After the presentations of the problems have been completed, I will provide the students with an opportunity to voice and discuss any difficulties that they encountered when completing these types of problems.

Attached to this section of this closing piece, there is a worksheet that can be used for homework or, you may want to use it as the independent exploration. I wanted to include it just to provide another resource.