L1 · Area of a parallelogram: base times height

Learning goal

“I can find the area of a parallelogram by multiplying its base by its perpendicular height - and I can explain, with the rearrangement model, why the slanted side is not used.”

Area — the amount of surface a shape covers, measured in square units (cm2, m2).

Base — the side of the parallelogram you choose as the bottom; any side can be the base.

Height — the perpendicular distance from the base to the opposite side - a straight, square-corner drop, never measured along the slant.

Parallelogram — a four-sided shape with both pairs of opposite sides parallel and equal.

Worked example

A parallelogram drawn on grid paper: base 8 cm, height 5 cm, slanted side about 5.4 cm. Step 1: Cut a right triangle off the left end, cutting straight down along the height (5 cm). Step 2: Slide that triangle to the right end. It fits exactly against the slanted side. Step 3: The new shape is a rectangle. Its length is the old base, 8 cm. Its width is the old height, 5 cm. Step 4: No squares were added or lost, so the areas are equal: Area of parallelogram = base x height = 8 x 5 = 40 cm2. Say it plainly: the slanted side disappears in the rearrangement - it is never used.

Check yourself — explain it

Why do we multiply base x height, and not base x slanted side?

Paired problem — example still visible

Base 7 cm, height 4 cm, slanted side 5 cm. -> A = 7 x 4 = 28 cm2

Faded completion — last step is yours

"Base 9 cm, height 3 cm: A = 9 x ___ = ___ cm2" -> 3; 27 cm2

Ready to practise?

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

Start practice →Take the unit quiz