Area of a composite rectangle is found by partitioning a rectilinear figure into non-overlapping rectangles, determining each rectangle’s area as length × width, and adding the partial areas; missing side lengths may be inferred from the figure’s given total lengths. The understanding includes preserving square units, avoiding overlap or gaps, and distinguishing area from perimeter. The scope is limited to figures composed of rectangles with whole-number measurements, not arbitrary polygons, decimal or fractional dimensions, or generalized algebraic formulas.
To find the area of a composite rectangle, split the figure into smaller rectangles that:
Then find each rectangle’s area using
Finally, add the smaller areas. Always use square units for area.
Example
An L-shaped figure is 10 units wide and 8 units tall. Its left section is 4 units wide, and the bottom strip is 3 units tall.
Partition it into two rectangles:
First, find the width of Rectangle B. The whole width is 10 units, and Rectangle A uses 4 units:
So Rectangle B is units by units.
Find each area:
Add the partial areas:
The area of the composite rectangle is
This is area because we counted the space inside the figure, not the distance around its outside edge.
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