Finding Area by Decomposing Rectangles
Finding Area by Decomposing Rectangles is a Grade 3 math skill from Eureka Math using the additive property of area to find total area of composite shapes. When a figure can be broken into two or more non-overlapping rectangles, the total area equals the sum of each smaller rectangle's area (A_total = A1 + A2). Third graders decompose L-shapes and other composite figures into simpler rectangles, calculate each area by multiplying length by width, then add the results. This skill is foundational for area problems involving irregular shapes.
Key Concepts
The total area of a composite shape ($A {total}$) is the sum of the areas of its smaller, non overlapping rectangular parts ($A 1$, $A 2$, etc.). This is known as the additive property of area. $$A {total} = A 1 + A 2$$.
Common Questions
What is the additive property of area?
The total area of a composite shape equals the sum of the areas of its non-overlapping rectangular parts. If you split a shape into rectangles, add their areas to find the total.
How do you find the area of an L-shaped figure?
Decompose the L-shape into two non-overlapping rectangles. Calculate each rectangle's area by multiplying length × width, then add the two areas together.
Why can you split a shape into smaller rectangles to find area?
Because the area covered by the whole shape equals the combined area covered by all its parts. Decomposing into rectangles makes multiplication possible where direct measurement would be complex.
What formula is used for each smaller rectangle when decomposing?
Area = length × width for each individual rectangle. The total area is then A1 + A2 (or A1 + A2 + A3 for three rectangles).
In which textbook is Finding Area by Decomposing Rectangles taught?
This skill is taught in Eureka Math, Grade 3.