mathsGrade 6-82 min read

Area and perimeter of every shape they'll ask

The formulas on one page, the difference students keep mixing up, and the two-step trick for any awkward compound shape.

Half the marks lost in this topic aren't formula mistakes — they're students computing area when the question asked for perimeter, or forgetting that area is measured in square units. Sort those two things out and the rest is substitution.

The one distinction to never forget

Perimeter is the distance around the edge. You walk it. Units are plain: cm, m.
Area is the space inside. You'd tile it. Units are squared: cm², m².

If your answer to an area question has no little $^2$ on the unit, it's wrong before anyone checks the number.

The formulas

Shape	Area	Perimeter
Rectangle	$l \times w$	$2(l + w)$
Triangle	$\tfrac{1}{2}\,b\,h$	add the three sides
Circle	$\pi r^2$	$2\pi r$ (circumference)
Parallelogram	$b \times h$	add the sides

For the triangle, $h$ is the perpendicular height — straight up from the base, not a slanted side. For the circle, the perimeter has its own name, circumference.

Worked example

A circle has radius $7\,\text{cm}$ (take $\pi \approx \tfrac{22}{7}$ ).

\text{Area} = \pi r^2 = \tfrac{22}{7}\times 7^2 = 154\ \text{cm}^2

\text{Circumference} = 2\pi r = 2\times\tfrac{22}{7}\times 7 = 44\ \text{cm}

Compound shapes: cut them up

An L-shape or a "rectangle with a bite out" isn't a new formula. Split it into shapes you know, find each, then add or subtract:

Slice the shape into rectangles (or a rectangle minus a circle, etc.).
Find the area of each piece separately.
Add the pieces — or subtract the cut-out hole.

Label the height you actually use. The single most common triangle error is using a slanted edge as the height. Draw the right-angle from the base and use that line.

Last revised 14 January 2025.