Math With Mr DJ

Grade 6 · Geometry · 6.G.A.1

Area by Composing & Decomposing Worksheets

Free, printable, and ready to teach: a practice worksheet, homework, an exit ticket, and an answer key with step-by-step solutions — plus lesson slides you can edit. No sign-up needed.

First page of the area by composing & decomposing practice worksheet Open the practice worksheet

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PDFs print on US Letter paper. Free for classroom and home use.

Watch: Perimeter and Area of Rectangles Explained
Key idea

Triangle: (b × h) ÷ 2. Rectangle and parallelogram: b × h. Trapezoid: average the parallel sides, then × height. For an odd shape, either decompose it into simple pieces and add, or compose a big rectangle and subtract the missing part.

Sample problems

  1. Find the area of a triangle with base 10 and height 6.
  2. Find the area of a triangle with base 7 and height 4.
  3. Find the area of a rectangle 9 by 5.
  4. Find the area of a parallelogram with base 15 and height 8.

Common mistakes to watch for

  • Answered 40 — forgot to halve. Every triangle area ends with a division by 2.
  • Halved it to 42 by over-applying the triangle rule.
  • Multiplied 6 × 10 × 4, or added the parallel sides without averaging.

The answer key explains each one, so you can tell what a wrong answer means.

How to use this set

  1. Teach with the slides (about 15 minutes), or watch the video together.
  2. Practice with the worksheet. Questions climb from fluency to application to reasoning.
  3. Check understanding with the exit ticket, and send the homework home.
  4. Mark with the answer key — each answer shows the steps and the most likely mistake.

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