Rectangles with the Same Area
Rectangles with the Same Area is a Grade 3 math skill from Eureka Math demonstrating that different rectangles can have identical areas. Area is the total count of unit squares covering a shape. Multiple rectangles with different dimensions can be formed using the same number of unit squares—for instance, a 3 × 8 and a 4 × 6 both have area 24 square units. This concept expands students' thinking beyond a single formula application to seeing that area measures quantity of space, not just a specific shape.
Key Concepts
The area of a shape is the total count of unit squares covering it. Rectangles with different dimensions can be formed using the same number of unit squares and will therefore have the same area.
Common Questions
Can two rectangles with different dimensions have the same area?
Yes. For example, a 2 × 12 rectangle and a 3 × 8 rectangle both have an area of 24 square units, even though their side lengths are different.
How do you prove two rectangles have the same area?
Calculate the area of each using Area = length × width. If both products are equal, the rectangles have the same area.
Why can different rectangles have the same area?
Because area depends on the total number of unit squares, not on the specific dimensions. Different factor pairs that multiply to the same product produce rectangles with equal area.
List all rectangles with whole-number sides that have an area of 12 square units.
1 × 12, 2 × 6, 3 × 4 (and their rotations: 12 × 1, 6 × 2, 4 × 3). All have area = 12 square units.
In which textbook is Rectangles with the Same Area taught?
This skill is taught in Eureka Math, Grade 3.