Area & Perimeter – Quick Reference Cards

Square

Area

A = a^2

Perimeter

P = 4a

Rectangle

Area

A = a \cdot b

Perimeter

P = 2(a + b)

Triangle

Area

A = \frac{1}{2} b \cdot h

Perimeter

P = a + b + c

Parallelogram

Area

A = b \cdot h

Perimeter

P = 2(a + b)

Trapezoid

Area

A = \frac{(a+b)}{2} \cdot h

Perimeter

P = a + b + c + d

Circle

Area

A = \pi r^2

Circumference

C = 2\pi r

Real-World Connections

Every formula above has a practical use. Here are common examples:

Shape	Real-world object	Why area matters
Square	Floor tiles, paving slabs, Post-it notes	Calculating how many tiles to order
Rectangle	Room floors, football pitches, window panes	Flooring, turf, glass cutting
Triangle	Roof gable ends, road warning signs, sails	Cladding material, reflective sheeting
Parallelogram	Decorative wall tiles, solar panel arrays	Estimating material quantities
Trapezoid	Swimming pool cross-section, field plots, dam faces	Water volume, soil and concrete quantities
Circle	Pipes, wheels, round table tops, manhole covers	Sealing, covering, cutting circular material

Real world: football pitch turf

A standard football pitch is 105 m × 68 m (rectangle). Area of turf needed:

$A = 105 \times 68 = 7{,}140 \text{ m}^2$

Groundskeepers order fertiliser, seed, and irrigation systems based on this figure.

Real world: paint for a triangular gable end

A house gable end is an isosceles triangle with base 8 m and height 3 m.

$A = \dfrac{1}{2} \times 8 \times 3 = 12 \text{ m}^2$

With two gable ends: $2 \times 12 = 24 \text{ m}^2$ — this is converted into litres of paint needed.

Real world: circumference of a roundabout

A roundabout has a radius of 15 m. The outer edge length (circumference):

$C = 2\pi \times 15 = 30\pi \approx 94.2 \text{ m}$

Road planners use this to calculate the length of kerbing and line markings to order.

Tip

When solving a real problem, always check what the area represents — is it a surface to be painted, a field to be planted, a floor to be tiled? The units (cm², m², km²) tell you the scale of the answer.

Real-World Shapes Around You

Every shape above appears in everyday life. Here are some examples to help you connect the formulas to the real world:

Shape	Where you see it
Square	Floor tiles, chessboard squares, sticky notes, window panes
Rectangle	Room floors, football pitches, phone screens, garden beds, books, door frames
Triangle	Roof gable ends, road warning signs, tent cross-sections, sails
Parallelogram	Decorative wall tiles, the side of a ramp, certain brick patterns
Trapezoid	Swimming pool cross-sections, dam cross-sections, road embankments, bucket outlines
Circle	Wheels, coins, pizza, the face of a clock, drain covers

Tip

Next time you are in a room, try to spot each shape — the floor (rectangle), the window (rectangle or square), a warning sign outside (triangle). Estimating areas in your head is a useful everyday skill.