Lesson 3Reasoning to Find Area
Learning Goal
Let’s decompose and rearrange shapes to find their areas.
Learning Targets
I can use different reasoning strategies to find the area of shapes.
Lesson Terms
- area
- decompose
- region
Warm Up: Comparing Regions
Problem 1
Is the area of Figure A greater than, less than, or equal to the area of the shaded region in Figure B? Be prepared to explain your reasoning.
![Square A, shaded. Square B identical to A, with a small shaded square removed in the middle and a small shaded square appended to its side.](../../../../../../embeds/5d838b6d--6.1.A3_Image_1.png)
Activity 1: On the Grid
Problem 1
Each grid square is 1 square unit. Find the area, in square units, of each shaded region without counting every square. Be prepared to explain your reasoning.
Are you ready for more?
Problem 1
Rearrange the triangles from Figure C so they fit inside Figure D. Draw and color a diagram of your work on the grid.
![blank grid](../../../../../../embeds/8707c5c0--6.1.A3.Image.00.Blank-Grid.png)
Activity 2: Off the Grid
Problem 1
Find the area of the shaded region(s) of each figure. Explain or show your reasoning.
Lesson Summary
There are different strategies we can use to find the area of a region. We can:
Decompose it into shapes whose areas you know how to calculate; find the area of each of those shapes, and then add the areas.
![Two images of a t-shaped object. The upper portion is 2 units tall and 6 units wide. The stem of the “t” is 4 units tall and 2 units wide. The second image is the same, except there is a line separating the upper portion and lower portion into two rectangles.](../../../../../../embeds/7df3309d--6.1.A3.Image.09a.png)
Decompose it and rearrange the pieces into shapes whose areas you know how to calculate; find the area of each of those shapes, and then add the areas.
![Two triangles next to each other making an irregular shape. One triangle is moved so the new shape is a rectangle.](../../../../../../embeds/03d307f3--6.1.A3.Image.10a.png)
Consider it as a shape with a missing piece; calculate the area of the shape and the missing piece, and then subtract the area of the piece from the area of the shape.
![Two shaded squares in a grid. Each are 6 units square and each as a 1 unit by two unit portion that is unshaded.](../../../../../../embeds/c3d305e0--6.1.A3.Image.11a.png)
The area of a figure is always measured in square units. When both side lengths of a rectangle are given in centimeters, then the area is given in square centimeters.
The area of this rectangle is 32 square centimeters.
![A blue rectangle with side lengths of 8 cm and 4 cm.](../../../../../../embeds/6e8bd904--6.1.A3_Image_12.png)