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AKS: 4MA.E.8 identify and draw geometric objects, classify polygons based on properties, and solve problems involving area and perimeter of rectangular figures.
Learning Targets: I can solve problems involving area and perimeter of composite rectangles.
Activating Strategy
Activating Strategy
Mini-Lesson
Mini-Lesson
We have learned how to apply the formulas for area and perimeter within rectangles. Area is the total space enclosed by the sides of a two-dimensional figure. Area is measured in square units. We can find the area of a rectangle by multiplying the length and width. Perimeter is the distance or length around a two-dimensional figure. We can solve the perimeter of a 2-dimensional figure by adding all of the side lengths.
Today, we will learn how to find the area of a composite rectangle by decomposing the figure into smaller rectangular regions. A composite rectangle is a plane shape or 2-dimensional figure whose sides meet to form right angles.
Listen as I think aloud...
Mark is building a new storage shed in his backyard. He has 200 square meters of space for the shed. A blueprint for the storage shed is pictured below. What is the area and perimeter of the shed? Does he have enough space in his backyard to build the shed?
When I read about this problem, the question asked me if Mark had enough space in his backyard for the storage shed. I’ll need to solve the area of the storage shed to answer this question because area tells the amount of space an object takes up.
The storage shed is an example of a composite rectangle because all corners are right angles, and I can partition this figure into smaller, non-overlapping rectangles.
Let’s use grid paper to support and represent the total area of the storage shed. Grid paper will help me visualize the square units that I’m measuring.
Each individual square on the grid paper represents one square meter, and each edge or side length of the square unit represents one meter.
Therefore, 10 meters will be 10 linear units on the grid paper, 5 meters will be 5 linear units, 6 meters will be 6 linear units, and 15 meters will be 15 linear units.
Now, let’s determine how to decompose this composite rectangle into smaller rectangles. The sum of the smaller rectangles will determine the total area of the shed.
We can find the area of each smaller rectangle and then compose those areas back together to find the total area of the storage shed.
I know that I can find the area of a rectangle by multiplying the length and width. I’m going to find the length and width of each smaller rectangle.
10 m x 5 m = 50 m2
4 m x 5 m = 20 m2
10 m x 5 m = 50 m2
50 m2 + 20 m2 + 50 m2 = 120 m2
When I combine or add the areas of the 3 rectangles, the total area is 120 square meters.
Therefore, the shed has an area of 120 m2.
Mark will have enough space to build the storage shed in his backyard because the shed has an area of 120 m2, and he has 200 m2 of space in his yard. 120 m2 is less than 200 m2.
50 m2 + 20 m2 + 50 m2 = 120 m2
To find the perimeter of Mark’s storage shed, he could add all of the side lengths around the figure together.
Find the sum of the 8 side lengths around the figure.
10 m + 15 m + 10 m + 5 m + 6 m + 5 m + 6 m + 5 m = perimeter
10 m + 15 m + 10 m + 5 m + 6 m + 5 m + 6 m + 5 m = 62 m
The perimeter of the shed is 62 meters.
Guided Practice
Guided Practice
Mathematicians, it is your turn to try!
Let’s model and solve another problem together on grid paper. Help me solve this one.
Guillaume helps plant a city garden in the park. What is the area of the garden? What is the perimeter?
Turn and talk with your elbow partner. Discuss how the composite shape of this garden could be decomposed into smaller rectangles to find the total area.
Is there more than one way to decompose it?
Discuss and draw the length of each side.
Draw the garden on grid paper.
Label the lengths of the composite rectangle.
What is one way we can decompose the figure into smaller rectangles? How can we find the area of this composite rectangular figure?
The area of the garden is 19 square meters.
Independent Task
Independent Task
1. FRECKLE - Complete THREE Freckle Assignments each week. DUE FRIDAY. Your HIGHEST score in Targeted Practice is your weekly math grade - Click HERE for Freckle website
GRADED Targeted Practice - Current skill (5 questions; Score Goal=80% or higher)
Fact Practice - Multiplication Fact Practice
Adaptive Practice - At YOUR level
2. iREADY Math - Complete 30 minutes at your level each week
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