Area of Irregular Polygons, Method 2

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Objective

SWBAT find the area of an irregular polygon.

Big Idea

Students create a larger figure to find the area of an irregular polygon.

Do Now

10 minutes

Students previously worked on finding the area of irregular polygons by dividing them into smaller regular polygons.  The Do Now Problem is a review of this concept.  I will encourage students to use the steps that they developed if they have trouble with the problem.

After about 5 minutes we will discuss the problem as a class.  I will select 2 students, who divided the shape differently, to show their work on there board.  This will enable students to see two different strategies.  

Mini Lesson

20 minutes

For this lesson, students will develop another method for finding the area of irregular polygons.  We will use the same Area of Irregular Polygons Mini Lesson Examples that was used for Method 1.  This will allow students to see that both methods are acceptable and they can choose which method to use.  Through a series of questions that I will ask students, they will develop a 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

What type of polygon is this?  Why?

Students should recognize that it is an irregular polygon.

Rather than divide the shape into smaller polygons, could we form a larger polygon that we have a formula for?

Students may suggest that we close the shape, horizontally at the bottom, to form a large rectangle. I will encourage them to draw and indicate this on the worksheet.

Do we have the length and width of this large rectangle?

We will look at the rectangle to verify that we have the necessary lengths and widths. The length is 6m and the width is 4 m.

What is the area of the large rectangle?

Students should apply the formula.

By closing the figure, we have created an "extra" rectangle? What is the area of this rectangle?

Students should find the dimensions of this rectangle and apply the area formula.

If we have the area of the larger figure and the area of the extra rectangle, what should we do to find the area of the original polygon?

Students should see that we need to subtract the areas for this method.

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

Method 2 Steps

1.  Create one large, closed figure 

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

3.  Find the area of the new, large figure

4.  Subtract the areas

5.  Label your answer

 

 

 

Independent Practice

10 minutes

Similarly to the lesson examples, students will complete the same problems as they did in the previous lesson, Area of Irregular Polygons Method 1.  Although they know the answers, there focus should be on using another strategy to correctly arrive at the same answer.

 

Each student will receive a Independent Practice Area of Irregular Polygons worksheet.  I will encourage students to use the steps that we developed to help them with their work.  If students have answers that differ from their method 1 answers, they should review their work.  Students often misidentify the value of a dimension.  Students may also discuss their work with their groups.

 

After 10 minutes, if students have questions or still didn't not arrive at the correct answers, we will discuss the problems as a class.

Lesson Review

5 minutes

As did method 1, 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.  We will also discuss the differences between the two methods.

 

Is it possible that you may have more than one shape to subtract from the larger figure?

Are the dimensions of the polygons always directly given?

How can you find the missing dimensions?

After you've found the area of the larger figure and the area of the smaller figures, what should you do?

How does this differ from the first method?

If done correctly, does it make a difference which method you use?

Are there times when one method may be easier to use rather than the other method?