Grade 6 Math: Area of Composite Figures
TL;DR: Composite figures are just simple shapes glued together, a rectangle joined to a triangle, an L-shape made of two rectangles, that kind of thing. To find the area, break the figure into pieces you recognize, calculate each piece’s area on its own, and add them up. If part of the figure is cut out, subtract that piece instead. You already know how to find the area of rectangles and triangles. This is just stitching those skills together.
Free tool: try the problems from this lesson in our Area & Perimeter Calculator.
Key takeaways:
- Composite figures are built from basic shapes: rectangles, triangles, trapezoids, circles, semicircles.
- Strategy 1: split the figure into shapes, find each area, then add.
- Strategy 2: surround the figure with a rectangle and subtract the missing pieces.
- Label each sub-shape’s dimensions clearly before doing arithmetic.
- Always include units squared (\(\text{cm}^2\), \(\text{in}^2\), etc.) in your final answer.
Grade 6 focus: A composite figure (or compound shape) is made from simpler figures, often rectangles and triangles. You find total area by adding areas of non-overlapping parts, or by subtracting a “cut-out” from a larger rectangle.
Video lesson: Watch this Math with Mr. J example of area for composite figures made from rectangles.
Strategy: Decompose
- Draw dashed lines to split the shape into rectangles/triangles you recognize.
- Label unknown lengths using properties of rectangles (opposite sides equal).
- Compute each area, then add (or subtract for holes).
Example (add regions)
An L-shape can split into two rectangles. Add their areas.
Example (subtract)
A rectangle with a rectangular hole: area = big rectangle − hole.
Explain your reasoning
Grade-level tasks often ask you to justify decompositions. Sketch, label, and show each area calculation.
Common mistakes
- Double-counting overlapping regions.
- Missing a hidden segment length needed for a sub-figure.
- Using perimeter where area is required.
Composite Figures: Complete Decomposition Guide
Master the systematic approach: identify basic shapes within the composite figure, separate them visually with dividing lines, calculate each area using standard formulas, and combine results. This method works for any complexity level. Examples include rectangle plus triangle (house shape), L-shapes created by subtracting one rectangle from another, and more complex multi-part figures.
Worked Examples with Full Reasoning
Rectangle plus triangle: 8×5=40 plus (1/2)x8x3=12 equals 52 cm². L-shaped figure: 12×10=120 minus 4×3=12 equals 108 cm². Trapezoid plus rectangle: 6×4=24 plus (1/2)(6+4)x3=15 equals 39 cm². Each example shows identifying shapes, calculating areas, and combining.
Review triangles, trapezoids, and compound figures for additional practice and related concepts.
Mastering Composite Figures: Decomposition Strategy
Composite figures are shapes constructed by combining two or more basic geometric forms like rectangles, triangles, circles, and trapezoids. Rather than seeking an obscure formula for an unusual shape, you employ decomposition: identify the basic shapes, calculate the area of each, and combine the results. This systematic approach works for any complexity level and teaches fundamental geometric reasoning.
The Decomposition Process
Begin by examining the composite figure carefully. Identify which basic geometric shapes comprise the overall figure. Visualize dividing lines that separate the composite figure into component shapes. Assign dimensions to each component based on the given measurements. Calculate the area of each basic shape using standard formulas. Add all areas together if combining shapes. Subtract removed areas if a piece has been cut out from a larger shape. Finally, verify that your units are correct (square centimeters, square inches, etc.) and that the final answer is reasonable given the figure’s approximate size.
Worked Example: Rectangle and Triangle Composition
A house-shaped figure consists of a rectangular base and a triangular roof. The rectangle measures 8 cm wide by 5 cm tall. The triangle sits on the rectangle’s top edge, with a base of 8 cm and height of 3 cm. Calculate the rectangle area: length times width equals 8 times 5 equals 40 cm². Calculate the triangle area: one-half times base times height equals one-half times 8 times 3 equals 12 cm². Add the areas: 40 + 12 equals 52 cm² total. This is the area of the entire house-shaped composite figure.
Worked Example: L-Shaped Figure Using Subtraction
An L-shaped courtyard can be calculated as a large rectangle with a smaller rectangular section removed from one corner. The outer dimensions are 12 meters by 10 meters, giving a large area of 120 m². The removed rectangular section measures 4 meters by 3 meters, with area 12 m². The L-shaped area equals 120 minus 12 equals 108 m². This method is often simpler than trying to separate the L into two rectangles when one section’s dimensions aren’t explicitly given.
Worked Example: Trapezoid and Rectangle Combination
A composite figure consists of a rectangle (6 cm by 4 cm) with a trapezoid attached to its top. The trapezoid has parallel sides of 6 cm (bottom, touching the rectangle) and 4 cm (top), with a height of 3 cm. Rectangle area: 6 times 4 equals 24 cm². Trapezoid area: one-half times (6 + 4) times 3 equals one-half times 10 times 3 equals 15 cm². Combined area: 24 + 15 equals 39 cm².
Common Composite Figure Patterns
House shapes combining rectangles and triangles appear frequently in geometry. L-shaped or stair-step figures use rectangular decomposition. Shapes with cut-out sections require subtraction of the removed area from a larger shape. Circular sections might be added or subtracted from rectangular bases.
Review our guides on triangles, trapezoids, and compound figures for additional practice and related concepts.
Mastering Composite Figures: Decomposition Strategy
Composite figures are shapes constructed by combining two or more basic geometric forms like rectangles, triangles, circles, and trapezoids. Rather than seeking an obscure formula for an unusual shape, you employ decomposition: identify the basic shapes, calculate the area of each, and combine the results. This systematic approach works for any complexity level and teaches fundamental geometric reasoning.
The Decomposition Process
Begin by examining the composite figure carefully. Identify which basic geometric shapes comprise the overall figure. Visualize dividing lines that separate the composite figure into component shapes. Assign dimensions to each component based on the given measurements. Calculate the area of each basic shape using standard formulas. Add all areas together if combining shapes. Subtract removed areas if a piece has been cut out from a larger shape. Finally, verify that your units are correct (square centimeters, square inches, etc.) and that the final answer is reasonable given the figure’s approximate size.
Worked Example: Rectangle and Triangle Composition
A house-shaped figure consists of a rectangular base and a triangular roof. The rectangle measures 8 cm wide by 5 cm tall. The triangle sits on the rectangle’s top edge, with a base of 8 cm and height of 3 cm. Calculate the rectangle area: length times width equals 8 times 5 equals 40 cm². Calculate the triangle area: one-half times base times height equals one-half times 8 times 3 equals 12 cm². Add the areas: 40 + 12 equals 52 cm² total. This is the area of the entire house-shaped composite figure.
Worked Example: L-Shaped Figure Using Subtraction
An L-shaped courtyard can be calculated as a large rectangle with a smaller rectangular section removed from one corner. The outer dimensions are 12 meters by 10 meters, giving a large area of 120 m². The removed rectangular section measures 4 meters by 3 meters, with area 12 m². The L-shaped area equals 120 minus 12 equals 108 m². This method is often simpler than trying to separate the L into two rectangles when one section’s dimensions aren’t explicitly given.
Worked Example: Trapezoid and Rectangle Combination
A composite figure consists of a rectangle (6 cm by 4 cm) with a trapezoid attached to its top. The trapezoid has parallel sides of 6 cm (bottom, touching the rectangle) and 4 cm (top), with a height of 3 cm. Rectangle area: 6 times 4 equals 24 cm². Trapezoid area: one-half times (6 + 4) times 3 equals one-half times 10 times 3 equals 15 cm². Combined area: 24 + 15 equals 39 cm².
Common Composite Figure Patterns
House shapes combining rectangles and triangles appear frequently in geometry. L-shaped or stair-step figures use rectangular decomposition. Shapes with cut-out sections require subtraction of the removed area from a larger shape. Circular sections might be added or subtracted from rectangular bases.
Review our guides on triangles, trapezoids, and compound figures for additional practice and related concepts.
Recommended EffortlessMath Books
For a workbook that covers area of every shape sixth graders see, the Mastering Grade 6 Math walks through rectangles, triangles, trapezoids, and composite figures with worked examples and practice sets. If you’re heading toward seventh-grade geometry (scale drawings, surface area, volume), Pre-Algebra for Beginners builds on the same foundation.
Frequently Asked Questions
How do you find the area of composite figures in 6th grade?
Break the figure into shapes you know, such as rectangles and triangles, find each area, and add them. If a piece is cut out, subtract it instead. For an L-shape made of a 10 cm by 6 cm rectangle and a 4 cm by 3 cm rectangle, the area is 60 + 12 = 72 cm². Label every side before you start calculating.
What are composite figures in grade 6?
A composite figure is a shape made by joining two or more simpler shapes. In grade 6 these are usually rectangles, squares, triangles and trapezoids, for example an L-shaped room or a house outline made of a square with a triangle roof. Seeing the simple shapes inside the figure is the first step to finding its area.
What is the formula for the area of composite figures in grade 6?
There is no single formula. The total area is the sum of the areas of the non-overlapping parts, using A = l × w for rectangles, A = ½ × b × h for triangles and A = ½(b₁ + b₂)h for trapezoids. For a 6 m by 4 m rectangle with a triangle on top that has base 6 m and height 3 m, the area is 24 + 9 = 33 m².
How do you use subtraction to find the area of a composite figure?
Draw one large rectangle around the whole figure, find its area, and subtract the missing piece. The same L-shape fits inside a 10 cm by 9 cm rectangle with a 6 cm by 3 cm corner missing, so its area is 90 − 18 = 72 cm². Getting the same answer by adding and by subtracting is a great way to check your work.
Where can I find area of composite figures grade 6 worksheets?
The practice problems with this lesson act as a grade 6 composite figures worksheet, with shapes to split, missing side lengths to find, and answers to check. When practicing, have your child sketch dashed lines showing how they split each shape and write the area of each piece, since many grade 6 tasks ask students to explain their method.
Related EffortlessMath Lessons
If a topic on this page feels rusty, these short lessons go deeper:
- How to find the area of rectangles
- How to find the area of triangles
- How to find the area of trapezoids
- How to find the area of a circle (resource currently unavailable)
- How to solve multi-step word problems
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