Unit 1, Lesson 3
Reasoning to Find Area
Grade 6
3.1
Warm-up
Comparing Regions
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.
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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.
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.
Find the area of the shaded region(s) of each figure. Explain or show your reasoning.
There are different strategies we can use to find the area of a region. We can:
Decompose it into shapes whose areas we know how to calculate. We find the area of each of those shapes, and then add the areas.
Decompose it and rearrange the pieces into shapes whose areas we know how to calculate. We find the area of each of those shapes, and then add the areas.
3 figures on grids with arrows pointing to the right between figures 1 and 2 and figures 2 and 3. On the left is an irregular figure. In the middle, the figure has been divided into two triangles with base = 3 units, height = 4 units. the triangle on the right has been moved 3 units left and 2 units down. On the right, rectangle made up of the two triangles from the figures on the left and in the middle. base = 3 units, height = 4 units.
Consider it as a shape with a missing piece. We calculate the area of the shape and the missing piece, and then subtract the area of the piece from the area of the shape.
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. For example, the area of this rectangle is 32 square centimeters.
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