L5 · Changing a dimension changes the area; reasonableness clinic

Learning goal

“I can predict and explain what happens to a rectangle's area and perimeter when its dimensions change (4.10), judge whether an area answer is reasonable (4.11), and rearrange area formulas to find a missing dimension (A1) - verifying by substitution every time.”

Dimension change — altering one or both side lengths of a rectangle and tracking the effect: doubling ONE dimension doubles the area; doubling BOTH multiplies the area by four, while the perimeter only doubles.

Isolate the unknown — rearranging a formula, using the same operation on both sides (preservation of equality), until the unknown stands alone: A = l x w becomes w = A / l.

Verify by substitution — putting the found value back into the ORIGINAL formula and checking that the stated area/perimeter comes out. An unverified isolation is a guess with good handwriting.

Worked example

Rectangle 4 m x 3 m: A = 12 m², P = 14 m. Change 1 - double the LENGTH only: 8 x 3 = 24 m² (area x 2); P = 2(8 + 3) = 22 m. Change 2 - double BOTH: 8 x 6 = 48 m² (area x 4); P = 2(8 + 6) = 28 m (perimeter x 2). The pattern, in words: area is a PRODUCT of two dimensions, so each doubled dimension contributes its own factor of 2 (2 x 2 = 4). Perimeter is a SUM, so doubling everything doubles the sum - once.

Check yourself — explain it

Doubling both sides multiplies the area by 4 because:

Paired problem — example still visible

Square, side 5 cm: A = 25 cm², P = 20 cm. Side doubles to 10 cm: new area and perimeter? -> A = 100 cm² (x 4); P = 40 cm (x 2)

Faded completion — last step is yours

"Rectangle 6 m x 2 m: A = 12 m². Halve the WIDTH: 6 x 1 = ___ m² - the area is ___ (doubled/halved/quartered)." -> 6 m²; halved

Ready to practise?

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

Start practice →Take the unit quiz

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

L5 · Changing a dimension changes the area; reasonableness clinic