Sixth Grade · Math · week 28

Finding area by decomposing shapes

Find the area of triangles, parallelograms, and irregular polygons by decomposing them into rectangles and triangles.

The area of a rectangle is length × width, a formula already known. Many other shapes can be measured using that same idea, broken into pieces.

A parallelogram has the same area as a rectangle with the same base and height: area = base × height. Cutting a triangle off one side and sliding it to the other turns the parallelogram into that rectangle.

A triangle is always exactly HALF of a parallelogram with the same base and height, so the area of a triangle is (base × height) ÷ 2. For an irregular polygon, split it into rectangles and triangles, find each area, then add them together.

📋 For the teacher
Teach it (10–15 min):
  • Cut a paper parallelogram and physically slide the triangle piece to make a rectangle - seeing it beats memorizing the formula.
  • Show that a triangle is HALF its matching parallelogram by folding or cutting a rectangle along its diagonal.
  • For irregular shapes, practice drawing a line to split the figure into familiar pieces before calculating anything.
  • Always label the answer "square units," since area covers two dimensions.
Talk about it:
  • Why does the parallelogram formula match the rectangle formula, base times height?
  • Why is a triangle's area formula half of the parallelogram formula?
  • How do you decide where to split an irregular shape into pieces?

Mastery looks like: They find the area of triangles, parallelograms, and composite shapes by decomposing into familiar pieces and applying the correct formulas.

Common stumbles: Forgetting to divide by 2 for a triangle; using the slanted side instead of the perpendicular height; forgetting to add all the decomposed pieces together.

Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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