Area of Triangles & Parallelograms
Find the area of parallelograms and triangles by relating them to rectangles: rearrange a parallelogram (cut off a triangle and move it) into a rectangle with the same base and perpendicular height; see a right triangle as half of a rectangle and any triangle as half of a parallelogram (or as two right triangles); use the resulting formulae A = b × h for parallelograms and A = ½ × b × h for triangles, always using the perpendicular height rather than a slanted side, including when the height falls outside an obtuse triangle; and recognise when an area formula can be used (rectangles, parallelograms, triangles) and when another method is needed, such as counting or estimating squares for an irregular shape
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Area of Triangles & Parallelograms means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.
Materials: Paper strips or a folded circle; Pencil and labels (1/2, 1/4). Adult folds a strip into halves and labels 1/2. Child makes three fair shares (halves/quarters) and names each piece. Done: three correctly named equal parts. Stop after the fresh check; keep optional challenge for another day.
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Learning resources
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Illustrative Mathematics · Practice link — not the full lesson
Same Base and Height, Variation 1
Before you open · source notes
Same base and height supports area of triangles and parallelograms. Not every perimeter-only worksheet.
Free, no sign-in. A teacher solution is on the same page, so use the student view with your child.
Before you openAsk the learner why two shapes with the same base and height have related areas.
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Source, access and review notes
Public Illustrative Mathematics task page. The .html address responds HTTP 308 to this URL. An anonymous GET of this URL on 2026-11-12 returned HTTP 200 with no login or payment prompt. Where a teacher solution is present, it is on the same page as the student task; this check did not find a separate locked student view. An adult can use the student view section and should not read a solution aloud. Advertising was not observed in the fetched HTML text; that is not a browser, device, or ad-free guarantee. This is a paper or discussion task, not an automatically marked interactive game. Opening the link does not save practice or assess mastery. Diagrams on the page use missing or filename-only alt text, so they are not an accessible image equivalent. Accessibility still depends on an adult describing the picture.
Illustrative Mathematics. “Same Base and Height, Variation 1.” Licensed CC BY-NC-SA 4.0. External task; Gakuva does not copy, host, embed, or redistribute it.
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Check understanding
- Cut a right-angled triangle off one end of a parallelogram with base 8 cm and perpendicular height 5 cm, move it to the other end to make an 8 cm × 5 cm rectangle, and state the area as 40 cm²
- Show that a right triangle with legs 6 cm and 4 cm is half of a 6 cm × 4 cm rectangle (12 cm²), and that an obtuse triangle with base 12 cm and perpendicular height 7 cm, drawn outside the triangle, is half of a parallelogram (42 cm²)
- Decide that a formula gives the area of a parallelogram with base 10 cm and perpendicular height 5 cm (50 cm², not the 60 cm² from its slanted 6 cm side) but not of an irregular leaf shape, whose area must be estimated by counting squares
“If your child is cutting triangular pieces of cloth where the base is 8 cm and the height is 5 cm, can they use a formula to work out the area of each piece?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Measurement
- Age range
- Ages 10–13
Standards