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

Grade 10 › T3U04 Area & Surface Area › L2
GRADE 10 · ALBERTAOUTCOME AB-MAT10-3-M4

L2 · Area of regular, composite and irregular 2-D shapes, including circles

Learning goal

“I can find exact areas with formulas - rectangles, triangles, parallelograms and circles - split composite shapes into pieces I know (or subtract a missing piece), and handle fractional side lengths without rounding until the final step.”

Composite shape — a flat shape built from two or more simple shapes (an L-shaped room, a wall with a gable). It has no single formula - you build its area from pieces.
Decompose — to split a shape into pieces whose areas you can compute. The partner move is SUBTRACTING a piece: area of the whole minus a cut-out.
Semicircle — exactly half a circle. Its area is half of πr²: find the full circle's area from the radius, then halve it.
Worked example

An L-shaped room: the bounding rectangle is 6 m x 4 m, with a 2 m x 2 m corner missing (a closet notch). Method 1 (subtract): whole 6 x 4 = 24 m², minus the notch 2 x 2 = 4 m² -> 20 m². Method 2 (split): a 6 m x 2 m strip (12 m²) plus a 4 m x 2 m block (8 m²) -> 20 m². The methods agree because area is conserved: cutting a shape into pieces - or imagining it completed - never changes the total surface.

Check yourself — explain it

Why does splitting a composite shape into pieces give the correct total area?

Paired problem — example still visible

A house shape: rectangle 8 cm x 5 cm with a triangle on top (base 8 cm, height 3 cm). Total area? -> 52 cm² (40 + 1/2 x 8 x 3 = 40 + 12)

Faded completion — last step is yours

"Parallelogram: base 9 cm, height 6 cm. A = b x h = 9 x ___ = ___ cm²." -> 6; 54 cm² (the height is the PERPENDICULAR height - a parallelogram is a rectangle in disguise, sheared.)

Ready to practise?

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

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