L3 · Area of a triangle: half the parallelogram

Learning goal

“I can find the area of a triangle by computing the area of the parallelogram with the same base and height and taking half - because two matching triangles fill it exactly.”

Diagonal — a line from one corner of a parallelogram to the opposite corner; it cuts the parallelogram into two matching triangles.

Congruent — exactly the same size and shape; the two triangles made by a diagonal are congruent, so their areas are equal.

Vertex — a corner of a shape; a triangle's height is measured from the vertex opposite the base.

Height (of a triangle) — the perpendicular distance from the base to the opposite vertex - still measured at a square corner, never along a slanted side.

Worked example

A triangle with base 8 cm and height 6 cm. Step 1: Complete the parallelogram: same base 8 cm, same height 6 cm. Its area is 8 x 6 = 48 cm2. Step 2: A diagonal splits that parallelogram into two congruent triangles. Step 3: Each triangle is exactly half: A = 48 / 2 = 24 cm2. Formula: A = b x h / 2. Say it plainly: the / 2 is not decoration - it is there because the triangle is half of the same-base, same-height parallelogram.

Check yourself — explain it

Why does the triangle formula divide by 2?

Paired problem — example still visible

Base 10 cm, height 4 cm. -> Parallelogram would be 40 cm2, so the triangle is 40 / 2 = 20 cm2

Faded completion — last step is yours

"Base 7 cm, height 6 cm: A = 7 x 6 / ___ = ___ cm2" -> 2; 21 cm2

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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