Area of Irregular Polygons, Method 1

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Objective

SWBAT find the area of irregular polygons.

Big Idea

Students divide irregular polygons into smaller shapes to find the area.

Do Now

10 minutes

For this lesson it will be important that students understand and are comfortable with using the area formulas.  The Area of Polygons Do Now will assess their understanding and give students a chance to review the concept.

Students may have difficulty with problem 1 because it has decimals.  This problem combines the concepts of geometry and number sense and students may not use the multiplying decimals algorithm correctly.

Students may have have difficulty with the second problem because there is extraneous information.  Students often feel that they have to use all the given information and they might mistakenly use the diagonal side as the height.

Before students begin, I will remind them that there is an algorithm for multiplying decimals   Also, I will remind them that problems sometimes have extra information and that as part of solving the problem, they need to sort out the important information.

Mini Lesson

20 minutes

For this lesson, students will find the area of irregular polygons by separating it into smaller identifiable regular polygons.  Through a series of questions that I will ask students, they will develop steps that will be useful for finding the area of irregular polygons.

Each student will receive an Area of Irregular Polygons Mini Lesson Examples

Example 1

Do we have an area formula for this polygon?  Why not?

Students should recognize that it is not a regular polygon and therefore we don't have a formula for it.  I will introduce the category of irregular polygons.

Is there a way we can use regular polygons to help us?

The advanced students may suggest that we divide the shape into smaller shapes.  It is important for students to recognize that they may choose to divide the shape differently from someone else, but they should arrive at the same answer.  For this example, we will divide the shape horizontally.

What polygons can we divide this shape into?  How many?

Students should suggest 3 rectangles.  I will encourage them to draw and indicate this on the worksheet.

As part of showing our work, how can we differentiate between the rectangles?

Students may suggest that we label the rectangles.  

Do we have all the lengths and widths of these rectangles?

We will look at each rectangle to verify that we have the necessary lengths and widths.  I will explain to students that sometimes the dimensions of a shape are not directly given and they will have to calculate the dimension.

Now that we have the dimensions of the rectangles, what should we do?

Students should see that we are ready to find the area of the rectangles.

How can we use these areas to find the area of the irregular polygon?

Students should share that the final step is to add the areas of the rectangles.

At this point, students have developed steps for finding the area of irregular polygons.  I will formalize these steps for them.

Method 1 Steps

1.  Divide the figure into smaller figures  (that you know how to find the area of) 

2.  Label each small figure and label the new lengths and widths of each shape

3.  Find the area of each shape 

4.  Add the areas

5.  Label your answer

We will continue and discuss and work through examples 2 and 3 together. 

Independent Practice

10 minutes

Students will receive the Independent Practice Area of Irregular Polygons Problems.  They will have about 10 minutes to complete the problems independently.  I will encourage them to use the steps that they developed to help them.

Students are grouped homogeneously by skill level, based on a previous exit ticket.  As students work, I will focus on helping the lower math level groups who may struggle with finding the missing dimensions of the smaller polygons.

After 10 minutes, students will discuss and share their answers with their group.  This will give students an opportunity to see that even if they divided the irregular polygon differently, they should have the same answers.  If there is any confusion or questions that students can't clarify among their groups, we will discuss them as a class.

Lesson Summary

5 minutes

This method for finding the area of irregular polygons involves a lot of steps, so for the lesson review we will discuss and review the steps.

 

Is it possible that you can divide the polygon into different shapes than someone else?

Are the dimensions of the smaller polygons always directly given?

How can you find the missing dimensions?

After you've found the area of the smaller shapes, what should you do?