L4 · Composite area

Learning goal

“I can find the area of a composite shape by splitting it into parallelograms and triangles I already know, finding each part's area, and adding - without counting any part twice.”

Composite shape — a shape made by joining two or more simpler shapes.

Decompose — to split a composite shape into simpler parts whose areas you can find.

Section — one part of the split; each section is counted exactly once.

Worked example

A garden plot is made of two sections joined together: a rectangle 8 m long and 5 m wide, and next to it a parallelogram with base 8 m and height 3 m (the parallelogram sits on the rectangle's 8 m side). Step 1: Decompose. The split line is the shared 8 m side. Step 2: Rectangle: 8 x 5 = 40 m2. Parallelogram: 8 x 3 = 24 m2. Step 3: The sections do not overlap, so total area = 40 + 24 = 64 m2. Say it plainly: composite area is just area, one section at a time - then add.

Check yourself — explain it

Why do we add the two section areas?

Paired problem — example still visible

A house front: a rectangle 6 m wide and 3 m tall (walls), with a triangular roof of base 6 m and height 4 m on top. -> Walls 6 x 3 = 18 m2; roof 6 x 4 / 2 = 12 m2; total 30 m2

Faded completion — last step is yours

"A mat: rectangle 12 cm x 5 cm plus a triangle with base 12 cm and height 2 cm. Rectangle = 60 cm2; triangle = 12 x 2 / 2 = ___ cm2; total = ___ cm2" -> 12 cm2; 72 cm2

Ready to practise?

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

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