Find Area by Decomposing into Rectangles
Find Area by Decomposing into Rectangles is a Grade 3 math skill from Eureka Math applying the additive area property to composite figures. Any composite figure can be split into two or more non-overlapping rectangles. The total area equals the sum of all those rectangles: A_total = A_rectangle1 + A_rectangle2. Students choose where to make the cuts, calculate each piece's area by multiplying its dimensions, then add the results. This strategy complements the subtraction approach and gives students flexible tools for measuring irregular shapes.
Key Concepts
To find the area of a composite figure, you can decompose (break) it into smaller, non overlapping rectangles. The total area is the sum of the areas of these smaller rectangles. $$A {total} = A {rectangle\;1} + A {rectangle\;2}$$.
Common Questions
How do you find the area of a composite figure by decomposing?
Split the composite figure into non-overlapping rectangles. Calculate each rectangle's area (length × width). Add all the areas: A_total = A1 + A2 + ...
How do you decide where to split a composite figure?
Look for a natural cut that divides the figure into two simpler rectangles. You can cut horizontally or vertically—choose the cut that makes the dimensions easiest to read.
Find the area of an L-shape that is 6 × 5 total with a 2 × 3 piece cut out.
Method 1 (decompose): Split into a 4 × 5 = 20 rectangle and a 2 × 2 = 4 rectangle. Total = 24. Method 2 (subtract): 30 - 6 = 24. Both give 24 sq units.
What formula applies when decomposing into two rectangles?
A_total = A_rectangle1 + A_rectangle2 = (l1 × w1) + (l2 × w2).
In which textbook is Find Area by Decomposing into Rectangles taught?
This skill is taught in Eureka Math, Grade 3.