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Section 15.2 · Geometry and measure

Compound shapes

Find the area and perimeter of shapes made from rectangles, by splitting them up or by subtracting from an enclosing rectangle.

6 teaching slides 53 practice questions Worked answers for every question

1 · Teaching slidesuse ← → keys

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2 · Key words

compound shapeA shape made from simpler shapes joined together.
splitCut a shape into pieces you can already work out.
enclosing rectangleThe smallest rectangle the shape fits inside.
L-shapeA rectangle with a rectangular corner removed.
borderA frame of constant width round a shape.

3 · Summary of the sectionrevise from this

  • A compound shape is built from rectangles, so it can always be handled with the rectangle formula.
  • Method 1 — split. Cut it into rectangles and add the areas.
  • Method 2 — subtract. Take the missing piece away from the enclosing rectangle.
  • Both methods must give the same answer. Doing one and checking with the other is free insurance.
  • Write every side length on the diagram first, including the ones you have to work out by subtracting.
  • For the perimeter, walk right round the outline. Inside joins are not part of it.
  • Cutting a rectangular corner out changes the area but not the perimeter.
  • A border of width b round an l by w picture makes the outside (l + 2b) by (w + 2b).
PDFPrintable worksheet All 53 questions, space to work PDFWorked answers Full solutions, not just the answer

Video lessons1 videos

Area of Compound Shapes

British corbettmaths

Splitting a shape into rectangles, and finding the side lengths that were not given.

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4 · Practice53 questions, easiest first

Previous

15.1 Perimeter and area of rectangles
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15.3 Units of area