6th grade composite area reasoning worksheets

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Use composite figures to find a total area, a component area or a missing dimension. Six questions combine rectangles and triangles, with different outlines and orientations. Difficulty changes the number of parts, the measurements supplied and the arithmetic required.

Free printable PDF worksheet, aligned to Common Core 6.G.A.1.

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The kind of problems you'll get

Find each requested measurement. Show your work and include units.

  1. A shape has area 30 cm²: a 3 × 4 rectangle and a triangle with base 6 and height h.

    Answer: 12 + 3 × h = 30, so h = 6 cm.

Most problems on this sheet sit beside a picture, model or diagram, so this is the worked example the sheet itself prints. The answer key on page two prints the answer under every problem.

Every print pulls a fresh set of problems at this level, so a make-up test or a second sibling never gets the same sheet.

What's on each sheet

Every version prints on US Letter or A4, with its answer key after the problems.

This sheet is one of the versions on the 6th grade area of composite figures page, with its own difficulty choices and its own answer key.

How to teach this

First decide whether the answer is an area or a length. For a missing component area, subtract the known areas from the total. For a missing rectangle dimension, divide the remaining area by the known side. For a triangle dimension, double its area before dividing by the known base or perpendicular height. A shared unknown may affect two regions; combine their contributions before solving. Check by substituting your answer. Use square units for areas and linear units for lengths.

Watch for: A triangle height must be perpendicular to its base; a slanted side is not its height. Missing dimensions use linear units, while total and component areas use square units.

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Aligned to Common Core 6.G.A.1. Reviewed by the One more sheet team. Content version 241, updated September 2026.

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