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Find the area of composite rectangles

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.

Detailed Explanation: Find the area of composite rectangles

To find the area of a composite rectangle, split the figure into smaller rectangles that:

  • do not overlap,
  • do not leave gaps, and
  • fit together to make the whole figure.

Then find each rectangle’s area using

Area=length×width\text{Area}=\text{length}\times\text{width}

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:

  • Rectangle A: the left section, 44 units by 88 units
  • Rectangle B: the lower-right section

First, find the width of Rectangle B. The whole width is 10 units, and Rectangle A uses 4 units:

104=610-4=6

So Rectangle B is 66 units by 33 units.

Find each area:

Area of A=4×8=32 square units\text{Area of A}=4\times 8=32\text{ square units} Area of B=6×3=18 square units\text{Area of B}=6\times 3=18\text{ square units}

Add the partial areas:

32+18=5032+18=50

The area of the composite rectangle is

50 square units\boxed{50\text{ square units}}

This is area because we counted the space inside the figure, not the distance around its outside edge.

Learn by doing: Find the area of composite rectangles

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Area of a Rectangle - Missing Square Corner


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