Day 14:

Area & Perimeter Composite Figures

with Grid Paper

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

Mystery Number

Use your Math Journal to solve

I am less than 100.
I have a factor of 3.
My ones digit is exactly 1 greater than my tens digit.
My tens digit is an odd number.
If you multiply my two digits, the product is a multiple of 8.
What number am I?

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...

Blaise had a piece of candy in his pocket. The wrapper of the candy is pictured below. What is the area and perimeter of the wrapper?

When I read this problem, the question asked me to figure out the area and perimeter of Blaise’s piece of candy in his pocket.

Area tells the amount of space an object takes up. Perimeter is the distance around the object.

The shape of Blaise’s piece of candy is an example of a composite rectangle because all of the corners are right angles, and I can partition this figure into smaller, non-overlapping rectangles.

Let’s use grid paper to represent the total area of the piece of candy. Grid paper will help me visualize the square units that I’m measuring.

Each square on the grid paper will represent one square centimeter. Each edge or side length of the square unit will represent 1 centimeter. So, 8 centimeters will be 8 linear units on the grid paper, 5 centimeters will be 5 linear units, 4 centimeters will be 4 linear units, and 3 centimeters will be 3 linear units.

On the grid paper, I can see that one of the lengths should be 2 centimeters. This makes sense since 2 centimeters and 3 centimeters are the same as 5 centimeters.

I can also see on the grid paper that a missing length is 4 centimeters. This makes sense because as I look vertically, 4 centimeters and another 4 centimeters are the same as 8 centimeters.

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 candy wrapper.

Decompose the composite rectangle. Choose a way:

We can find the area of each smaller rectangle and then compose those two areas back together to find the total area of the candy wrapper.

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.

4 cm x 5 cm = 20 cm2

4 cm x 3 cm = 12 cm2

20 cm2 + 12 cm2 = 32 cm2

When I combine or add the areas of the 2 rectangles, the total area is 32 square centimeters. Therefore, the candy wrapper has an area of 32 cm2.

To find the perimeter of the candy wrapper, he could add all the side lengths around the figure.

8 cm + 5 cm + 4 cm + 2 cm + 4 cm + 3 cm = perimeter

8 cm + 5 cm + 4 cm + 2 cm + 4 cm + 3 cm = 26 centimeters

The perimeter of the candy wrapper is 26 centimeters.

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.

Below is an outline for a small jewelry box that can hold earrings. Determine the area and perimeter of the jewelry box.

Let’s explore this together. Draw the outline of the jewelry box on your grid paper.

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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