Mathematics • Year 8 • Unit 3 • Lesson 4

Perimeter in the Real World

Use perimeter for fencing, picture framing, decking, an L-shaped vegie patch, and a council park. Then explain your thinking in your own words.

Apply · Real-World Maths

1. Word problems

Each problem uses perimeter for something practical — fencing, framing, edging. Draw a sketch, label all sides, and show working.

1.1 — Pool fencing. A rectangular pool area is 12 m long and 8 m wide. Council requires a fence around the entire perimeter. Fence panels are sold by the metre at $48 per metre.

(a) Calculate the perimeter.
(b) Calculate the total cost of fencing. 3 marks

Stuck? P = 2(12) + 2(8) = 24 + 16 = 40 m. Cost = perimeter × $48.

1.2 — Picture framing. Lucas wants to frame a square photo with side length 18 cm. Frame moulding costs $12 per metre.

(a) Find the perimeter of the photo in cm, then convert to metres.
(b) Calculate the cost of the frame moulding. 3 marks

Stuck? P = 4 × 18 = 72 cm = 0.72 m. Cost = 0.72 × $12. Watch the unit conversion (100 cm = 1 m).

1.3 — Vegie patch. Maria builds an L-shaped vegie patch: a 4 m × 3 m rectangle attached to a 2 m × 2 m square (sharing one full edge). She wants timber edging around the entire boundary of the L-shape.

(a) Sketch the L-shape with all sides labelled (including the missing sides).
(b) Calculate the perimeter of the L-shape — the total length of timber edging needed. 3 marks

Stuck? Total width = 4 m; total height varies. If the 2×2 sits ON TOP of one end of the 4×3 (sharing 2 m of the long edge), then total height = 3 + 2 = 5 m at that end, and there's a step of (4−2) = 2 m horizontally where the 2×2 ends. Trace the boundary carefully.

1.4 — Decking around a rectangular hot tub. A hot tub is 2.4 m long and 1.8 m wide. Tomas builds decking that surrounds the tub by an extra 1 m on all four sides (so the decking is 1 m wider on each side).

(a) Find the dimensions of the OUTER edge of the decking.
(b) Calculate the perimeter of the outer edge. 3 marks

Stuck? Each side of the tub gets 1 m extra, so add 2 m total to each dimension. Outer length = 2.4 + 2(1) = 4.4 m. Outer width = 1.8 + 2(1) = 3.8 m. P = 2(4.4) + 2(3.8).

1.5 — Council park walking track. A council L-shaped park has total dimensions 80 m × 60 m, with a 30 m × 20 m rectangular building footprint removed from one corner. They want to build a path that follows the entire outer boundary of the L-shape.

(a) Sketch the L-shape and find all 6 side lengths.
(b) Calculate the length of the walking track. 3 marks

Stuck? Missing horizontal = 80 − 30 = 50 m. Missing vertical = 60 − 20 = 40 m. Sides: 60, 80, 40, 30, 20, 50. Add them.

2. Explain your thinking

This question is about communication, not just answers. Use full sentences. 4 marks

2.1 A classmate calculates the perimeter of an L-shape that has total dimensions 10 m × 6 m with a 4 m × 2 m notch removed. They write: "P = 10 + 6 + 4 + 2 = 22 m." In your own words, explain (i) what mistake they have made, (ii) how to find the two missing sides correctly, and (iii) what the actual perimeter is, with full working. Use the phrase "an L-shape has six sides, not four" somewhere in your answer.

Stuck? Revisit lesson § Card 9 — they only added the 4 LABELLED sides and skipped the 2 missing sides. Missing horizontal = 10 − 4 = 6; missing vertical = 6 − 2 = 4.

How did this worksheet feel?

Got it Partly Lost

What I'll revisit before next class:

Answers — Do not peek before attempting

1.1 — Pool fencing

(a) P = 2(12) + 2(8) = 24 + 16 = 40 m.
(b) Cost = 40 × $48 = $1920.

1.2 — Picture framing

(a) P = 4 × 18 = 72 cm = 0.72 m.
(b) Cost = 0.72 × $12 = $8.64.

1.3 — Vegie patch L-shape (4×3 + 2×2 on top sharing 2 m edge)

(a) Tracing the boundary: across the top of the rectangle (4 m if the 2×2 sits flush against one end, the top goes 2 m to the start of the 2×2, then we step up 2 m, then across the top of the 2×2 for 2 m, then down 2 m to the rest of the top, but this configuration depends on placement). Most common reading: the 2×2 sits on top of one short end of the 4×3, sharing 2 m of the top edge. Then sides going clockwise from bottom-left: bottom = 4 m, right side = 3 m, top step-out = (4 − 2) = 2 m, up the side of the 2×2 = 2 m, top of the 2×2 = 2 m, down the LEFT of the 2×2 = 2 m (back to the rest of the top edge — but this is the SAME side that was the "step", so it's already accounted for). Simpler reading: total height at one end is 3 + 2 = 5 m; total height at the other end is just 3 m; total width is 4 m; the 2×2 adds a 2 m × 2 m bump on top at one end.
Sides (clockwise from bottom-left): bottom 4, right 3, step in 2, up 2, top of bump 2, left of bump down to rest 2, top of original 2, left side 3.
(b) P = 4 + 3 + 2 + 2 + 2 + 2 + 2 + 3 = 20 m of timber edging.

1.4 — Decking around hot tub

(a) Outer length = 2.4 + 2(1) = 4.4 m; outer width = 1.8 + 2(1) = 3.8 m.
(b) P = 2(4.4) + 2(3.8) = 8.8 + 7.6 = 16.4 m.

1.5 — Council park L-shape (80 × 60 with 30 × 20 cut)

(a) Missing horizontal = 80 − 30 = 50 m. Missing vertical = 60 − 20 = 40 m. Six sides: 60, 80, 40, 30, 20, 50.
(b) P = 60 + 80 + 40 + 30 + 20 + 50 = 280 m.

2.1 — Explain your thinking (sample response)

The classmate has only added the four side lengths that were given in the problem, but an L-shape has six sides, not four — they've ignored the two unlabelled sides on the inside of the notch. To find them, use the opposite-sides rule: the missing horizontal side equals the total width minus the partial width that's already given (10 − 4 = 6 m), and the missing vertical side equals the total height minus the partial height (6 − 2 = 4 m). So all six sides are 10, 6, 4, 2, 6, 4, and the actual perimeter is P = 10 + 6 + 4 + 2 + 6 + 4 = 32 m, not 22 m.

Marking: 1 mark for spotting "only 4 sides added"; 1 mark for correctly finding both missing sides (6 m and 4 m); 1 mark for the correct perimeter of 32 m; 1 mark for clear sentences using "an L-shape has six sides, not four".