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Compound shapes – practice for Years 5–7

Sample questions on Compound shapes with the right answer and a worked solution, from easy to hard. In the Pickles Academy app a child gets new questions of the same kind every time, so they can't just learn the answers by heart.

Subject
Maths
Year
Years 5–7
Curriculum area
Geometry and measures

Question types: Perimeter and area of a compound shape

Rule: Compound shapes

Area: split the shape into rectangles and add their areas, or take the cut-out corner away from the whole rectangle.

Perimeter: add all the sides round the shape; work out missing lengths from the opposite sides.

Example: A 10 × 5 cm rectangle without a 3 × 3 cm corner: A = 50 − 9 = 41 cm²

Watch out: A cut-out corner doesn’t make the perimeter smaller: it stays the same as for the whole rectangle.

Sample questions

  1. Question 1 Easy

    The shape was made by cutting a smaller rectangle from the corner of a rectangle; all its angles are right angles. Work out its perimeter.

    9 cm3 cm5 cm3 cm4 cm6 cm
    Show the solution
    Answer: 30 cm

    How it works: P = 9 + 3 + 5 + 3 + 4 + 6 = 30 cm

  2. Question 2 Normal

    The shape was made by cutting a smaller rectangle from the corner of a rectangle; all its angles are right angles. Work out its perimeter.

    14 cm7 cm3 cm7 cm
    Show the solution
    Answer: 42 cm

    How it works: The horizontal sides add up to 2 × 14, the vertical ones to 2 × 7; P = 14 + 4 + 7 + 3 + 7 + 7 = 42 cm

  3. Question 3 Hard

    The shape was made by cutting a smaller rectangle from the corner of a rectangle; all its angles are right angles. Work out its perimeter.

    14 cm4 cm7 cm7 cm
    Show the solution
    Answer: 42 cm

    How it works: The horizontal sides add up to 2 × 14, the vertical ones to 2 × 7; P = 14 + 4 + 7 + 3 + 7 + 7 = 42 cm

Related topics

All Maths topics

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