Perimeter measures the BOUNDARY — walk all the way around. Area measures the SPACE inside — how much floor it would take to cover it.
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Every flat-shape formula boils down to two ideas: adding up the sides (perimeter) or multiplying base by height (area).
📊 The core formulas
| Shape | Perimeter | Area |
|---|---|---|
| Rectangle | 2 × (length + width) | length × width |
| Square | 4 × side | side × side |
| Triangle | sum of all three sides | ½ × base × height |
| Parallelogram | 2 × (side1 + side2) | base × height |
Worked example: a rectangle 12 m by 8 m has perimeter = 2×(12+8) = 40 m, and area = 12×8 = 96 m².
A circle uses π (approximately 22/7), and a trapezium or rhombus each has its own special formula built from its unique shape.
📌 Special-shape formulas
Circle circumference = 2πr. Circle area = πr². For r=7 (using π=22/7): circumference=44, area=154.
Trapezium area = ½ × (sum of parallel sides) × height. Sides 10 and 14, height 6: ½×24×6=72.
Rhombus area = ½ × diagonal₁ × diagonal₂. Diagonals 10 and 24: ½×10×24=120.
Olympiad trap: when π is not given, always use 22/7 for whole-number radii that divide evenly by 7 — it gives an exact answer, unlike 3.14.
A path built AROUND a field is really just one big rectangle with a smaller rectangle cut out of the middle.
Worked example: a 20 m × 15 m field has a 2 m wide path built all around its OUTSIDE. The outer rectangle is 24 m × 19 m. Path area = (24×19) − (20×15) = 456 − 300 = 156 m².
12 questions on perimeter, area, circles and pathway problems.
