Ctrl+k

Find area of composite rectangles

Area of a composite rectangle figure is the total region covered, found by decomposing the figure into non-overlapping rectangles, multiplying each rectangle’s length by its width, and adding the partial areas; a missing section may also be subtracted from a larger enclosing rectangle. The reasoning connects area to multiplication and the distributive property, requires square units, and distinguishes area from perimeter while using whole-number side lengths rather than decimals, algebraic expressions, or non-rectilinear regions.

Detailed Explanation: Find area of composite rectangles

To find the area of a composite rectangle figure:

  1. Split the figure into smaller, non-overlapping rectangles, or find the area of a large rectangle and subtract a missing part.
  2. Find each rectangle’s area using
Area=length×width.\text{Area}=\text{length}\times\text{width}.
  1. Add the smaller areas, or subtract the missing area.
  2. Write the answer in square units.

Example: An L-shaped figure fits inside an 88-unit by 66-unit rectangle. A 33-unit by 22-unit rectangle is missing from the top-right corner.

Step 1: Find the area of the large rectangle.

8×6=48 square units8\times 6=48\text{ square units}

Step 2: Find the area of the missing rectangle.

3×2=6 square units3\times 2=6\text{ square units}

Step 3: Subtract the missing area.

48−6=42 square units48-6=42\text{ square units}

So, the area of the composite figure is

42 square units.\boxed{42\text{ square units}}.

We find area by covering the inside of the figure. Perimeter is different because it measures the distance around the outside.

Learn by doing: Find area of composite rectangles

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

    Practice with unlimited practice problems

    Area of a Rectangle - Missing Square Corner

      ?