Grade 7 › G7U07 Circles & Area

Grade 7 › G7U07 Circles & Area › L6
GRADE 7 · ALBERTAOUTCOME AB-G7-SS2

L6 · Area formulas: triangles and parallelograms

Learning goal

“I can explain where the formulas A = b x h (parallelogram) and A = b x h / 2 (triangle) come from, and I can apply them - using the perpendicular height, never a slanted side.”

Base — the side of a parallelogram or triangle chosen as the reference side (b); any side can serve, if paired with its own height.
Height — the PERPENDICULAR distance from the base to the opposite side or vertex (h). It meets the base at 90°; a slanted side is never the height.
Formula (area) — A = b x h for a parallelogram; A = b x h / 2 for a triangle.
Rearrangement — cutting a piece off a shape and moving it without changing the area, e.g. turning a parallelogram into a rectangle.
Worked example

A parallelogram has base 9 cm and perpendicular height 5 cm (its slanted side is 6 cm). Step 1: Cut the triangle off the left end and slide it to the right end. The shape becomes a rectangle - no paper added or lost, so the area is unchanged. Step 2: The rectangle's length is the parallelogram's base (9 cm) and its width is the parallelogram's perpendicular HEIGHT (5 cm) - not the slanted side, which becomes the cut edge, not a rectangle side. Step 3: A = b x h = 9 x 5 = 45 cm2. Say it plainly: the height is the measurement that survives the rearrangement. The slanted side is a decoy - it is never multiplied.

Check yourself — explain it

After the rearrangement, the rectangle's width equals the parallelogram's...

Paired problem — example still visible

Parallelogram: base 7 cm, height 3 cm, slanted side 4 cm -> A = 7 x 3 = 21 cm2

Faded completion — last step is yours

"Base 12 cm, height 4 cm: A = 12 x ___ = ___ cm2" -> 4; 48 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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