Grade 10 — Mathematics 10-3 › T3U04 Area & Surface Area

Grade 10 › T3U04 Area & Surface Area › L3
GRADE 10 · ALBERTAOUTCOME AB-MAT10-3-M4

L3 · Converting area units (built from linear conversions)

Learning goal

“I can convert area measurements between squared units - SI and imperial - by SQUARING the linear conversion factor (1 ft² = 144 in²), in both directions, including multistep conversions like yd² -> in².”

Area conversion factor — the number you multiply or divide by to change an area's unit. It is the SQUARE of the linear factor: lengths convert by 12, areas by 12^2 = 144.
Squared unit — a unit of area: in², ft², yd², cm², m². The little 2 is the whole lesson: two dimensions, two conversions.
Direction of conversion — converting toward a SMALLER unit makes the number bigger (multiply); toward a LARGER unit makes it smaller (divide). Check every conversion against this rule.
Worked example

Convert 3 ft² to in². Step 1 (build the factor): 1 ft = 12 in, so one square foot is a square 12 in by 12 in: 1 ft² = 12 x 12 = 144 in². The linear factor 12 is squared because the unit itself is squared. Step 2 (direction): in² is the SMALLER unit, so the number grows - multiply. Step 3: 3 x 144 = 432 in². Verify by the rule: 432 > 3 (smaller unit, bigger number).

Check yourself — explain it

Why is 1 yd² equal to 9 ft² and not 3 ft²?

Paired problem — example still visible

Convert 5 yd² to ft². -> 45 ft² (5 x 9)

Faded completion — last step is yours

"Convert 2.5 ft² to in²: 2.5 x ___ = ___ in²." -> 144; 360 in²

Ready to practise?

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

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