Lesson Topic The Area of Polygons Through Composition

Lesson Topic: The Area of Polygons Through Composition and Decomposition & Area in the Real World Lesson Objective: I can… Show the area formula for the regions bounded by polygons, including trapezoids, by decomposing the region into familiar polygons. Decompose rectangles to determine the area of other quadrilaterals. Determine the area of composite figures in real-life contextual situations using composition and decomposition of polygons and I can determine the area of a missing region using composition and decomposition of polygons.

Let’s Discuss… What is a polygon? What is a diagonal in a polygon? What does bisect mean? What is a trapezoid? What is an isosceles trapezoid? Right? Scalene? How do we find the area of a trapezoid?

Vocabulary: Composing – Joining or putting together Decomposing – Taking apart *We can calculate the area of an irregular figure by separating it into polygons we are familiar with, finding the area of each part, and adding them all together OR calculating the area of a larger familiar rectangle and subtracting a missing piece.

Opening Exercise Complete the rectangle that encloses the figure.

Example 1 The area of this figure can be found in at least 4 ways

Example 2: Decomposing Trapezoids

Example 3: Area in the Real World We want to paint a set of our cabinet doors with chalkboard paint. Let’s round the base and height to the nearest foot. If 1 bucket of paint will only cover 8 square feet, how many buckets of paint do we need to ask for? We need to make sure we round up to the nearest whole bucket (if necessary) as we cannot ask for a fraction of a bucket of paint. What if we had a poster that was 3 feet by 2 feet on one of the doors that could not be painted over?

Options for Practice: 1. 2. Use the information from example 3 to figure out how many buckets of chalkboard paint you would need for the top of your desk if you cannot paint underneath your handout. You will need a ruler. Be sure to round to the nearest foot. Pull up the exercise on today’s Power. Point on your i. Pad and record your work in your notebook or on a separate sheet of paper.

Exercise Use this information to find the area for the whole parallelogram.

Lesson Summary & Evaluate Your Learning Answer in complete sentences: 1 – What does it mean to decompose a polygon? 2 – Sometimes measurements are given in inches and area is calculated in square feet. How many square inches are in a square foot? 3 – How can you prove that we can find a trapezoid’s area by multiplying the average of its bases by its height? 4 – Write a situation of when you would need to use the area of a polygon in real life. How will you “Sharpen Your Saw”?