Area & perimeter mix-ups
Circles and compound shapes under the clock.
← All countdown tipsPerimeter is the fence — the distance around. Area is the grass inside. Mix them up and a 6 m × 4 m garden becomes “20” when they wanted 24, or “24” when they wanted 20. Read the last line: around, or covering?
Picture it: 6 m by 4 m rectangle
Area = 6 × 4 = 24 m²
Perimeter = 6 + 4 + 6 + 4 = 20 m
Remember — the method
- Underline “around / fence / border” (perimeter) or “cover / turf / paint / tiles” (area).
- Rectangle: area = l × w. Perimeter = 2(l + w).
- Compound shape: split into rectangles, add areas; for perimeter, only the outer edge.
- Units: area uses squared units (cm², m²). Perimeter does not.
Exam trap
Using length × width for a perimeter question, or adding all sides for an area question. The numbers 20 and 24 both look “about right” for a 6 by 4 — that is the trap.
✗ Fence = 6 × 4 = 24 m
That’s the grass, not the fence
✓ Fence = 20 m
Walk all four sides
Question patterns you might see
1 · Simple — Rectangle both ways
8 cm by 3 cm → area 24 cm², perimeter 22 cm. Write both so you don’t grab the wrong one from the options.
Area
24 cm²
→Perimeter
22 cm
2 · Simple — Square
Side 5 cm → area 25 cm², perimeter 20 cm. If they give the perimeter (20 cm), one side is 5 cm, then area is 25 cm².
3 · Medium — L-shape area
Top
24
→Stem
6
→Area
30 cm²
Split into two rectangles, add the areas. Do not add every labelled length for area.
4 · Medium — L-shape perimeter
Walk the outer path only. Inner “cut-out” edges that sit inside the original rectangle are not part of the fence.
Missing outer lengths: subtract the known piece from the full side, then add every outer edge.
5 · Trickier — Circle (use 3 for π if they say so)
Radius 7 cm, π ≈ 22/7 → circumference 2πr = 44 cm (perimeter of the circle). Area πr² = 154 cm². If they give diameter, halve it first.
r
7
→2πr
44 cm
→πr²
154 cm²
6 · Trickiest — Path around a lawn
Inner lawn 10 m by 8 m, path 1 m wide all round. Outer rectangle 12 m by 10 m. Path area = outer − inner = 120 − 80 = 40 m².
- 1Draw inner and outer rectangles.
- 2Add 1 m on both ends of each side (width + 2, length + 2).
- 3Subtract the inner area from the outer area.
Coach tip: scribble “fence or grass?” before you calculate. Units² means grass.
Tomorrow (D-9): theme and symbolism.
Next step
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