Triangle area: build the rectangle

Grade 6 mathematics · 15 minutes · Area

Derive triangle area from a rectangle and identify a perpendicular height.

Classroom activity

Draw a rectangle with base 8 cm and height 5 cm. Draw a diagonal between opposite corners.

1. Calculate the rectangle area. Explain why the diagonal creates two triangles of equal area.
2. Find the area of one triangle and write a rule using base b and height h.
3. A different triangle has base 10 cm and perpendicular height 6 cm. Find its area.
4. A sloping side is marked 8 cm. Explain why that length cannot simply replace the perpendicular height.

Use drawings or paper cutouts to justify the factor of one-half.

Check understanding

Find the area of a triangle with base 9 cm and perpendicular height 4 cm. Include units and explain the one-half factor.

Teacher guide and answers

The rectangle is 40 cm² and each triangle is 20 cm². A = 1/2 × b × h. The second triangle is 30 cm²; the exit answer is 18 cm². Height must be perpendicular to the chosen base. If learners confuse side and height, mark right angles. Extend by finding possible base-height pairs for area 24 cm².

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Grade 6 topic reference. Confirm your adopted standards; topic guidance does not certify alignment.