Grade 10 — Mathematics 10-3 › T3U03 Linear Measurement Problems

Grade 10 › T3U03 Linear Measurement Problems › L3
GRADE 10 · ALBERTAOUTCOME AB-MAT10-3-M3/A1

L3 · Perimeter, circumference, and length + width + height problems

Learning goal

“I can solve perimeter, circumference, and shipping (length + width + height) problems, choose the right operation before I compute (3.6), and rearrange the perimeter and circumference formulas to find a missing dimension (A1).”

Perimeter — the total distance AROUND a flat shape: the sum of all its side lengths. For a rectangle, P = 2(l + w) - two lengths and two widths.
Circumference — the perimeter of a circle: the distance around it. C = πd, or C = 2πr. It is a LENGTH (cm), never an area.
Length + width + height (L + W + H) — the shipping measure: carriers add a parcel's three dimensions. It is not a volume and not a perimeter - just the sum of the three edges that meet at one corner.
Worked example

A rectangular garden is 6.5 m long and 4 m wide. Fencing goes all the way around. How much fencing? Step 1 (choose the operation, 3.6): Fencing runs AROUND - this is perimeter, a sum of sides. Not length x width; that is the covering (area), a different job. Step 2: P = 2(l + w) = 2(6.5 + 4) = 2 x 10.5. Step 3: P = 21 m. Verify by the long way: 6.5 + 4 + 6.5 + 4 = 21.

Check yourself — explain it

You are buying baseboard for a room 5 m by 3.5 m. Your plan should be:

Paired problem — example still visible

A deck is 4.8 m by 3.6 m. Railing goes on all four sides. How much railing? -> 16.8 m (2 x (4.8 + 3.6) = 2 x 8.4)

Faded completion — last step is yours

"Picture frame, 45 cm by 30 cm: P = 2(45 + ___) = 2 x 75 = ___ cm." -> 30; 150 cm

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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