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 PowerPoint
on your iPad 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”?