Common areas and perimeters: the cheat sheet

The cheat sheet

Shape	Perimeter	Area
Rectangle ($L, w$)	$2(L + w)$	$L \times w$
Square ($c$)	$4c$	$c^2$
Triangle (sides $a, b, c$, height $h$)	$a + b + c$	$\dfrac{\text{base} \times h}{2}$
Equilateral triangle ($c$)	$3c$	$\dfrac{c^2 \sqrt{3}}{4}$
Parallelogram (base $b$, height $h$)	$2(b + \text{side})$	$b \times h$
Trapezoid ($B, b$, height $h$)	sum of 4 sides	$\dfrac{(B + b) \times h}{2}$
Rhombus ($c$, diagonals $D, d$)	$4c$	$\dfrac{D \times d}{2}$
Circle / Disk (radius $r$)	$2\pi r$	$\pi r^2$

Mnemonics

• Trapezoid: “average of bases times height”
• Rhombus: “half product of diagonals”
• Triangle: half of a rectangle
• Circle vs disk: circle = boundary (perimeter), disk = interior (area)

Units

• Perimeter: cm, m, km
• Area: cm², m², km²
• Watch conversions: 1 m² = 10,000 cm² (not 100!)

Common mistakes

1. Confusing area and perimeter.
2. Not using the HEIGHT in a triangle: height is perpendicular to base.
3. Using diameter instead of radius for circles.

?À toi de jouer

Area of a trapezoid with bases 6 and 10, height 4?

A.32B.40C.20D.64

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