An L-shape is made by joining a 6 cm by 4 cm rectangle to a 5 cm by 3 cm rectangle (with no overlap). What is the total area of the L-shape?
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Practise IGCSE 0580 questions in the style of recent Extended past papers, organised by syllabus subtopic. Each set comes with an examiner-style mark scheme and a downloadable worksheet.
These Compound shapes and parts of shapes Topical Past Paper Questions are written in the style of recent Cambridge IGCSE Mathematics 0580 Extended papers and grouped by the Mensuration (E5.5) section of the 2025–2027 syllabus. Use them to revise the exact skills examiners test in this part of the course.
Each question is graded Easy → Medium → Hard, plus an A★ Challenge for top-grade preparation. Tap a question to mark your own answer, then unlock the examiner-style mark scheme with model solutions and examiner tips. A printable Topical Past Papers worksheet is included so you can practise offline.
Find perimeters, areas and volumes of compound 2-D and 3-D shapes formed by combining or subtracting standard shapes.
An L-shape is made by joining a 6 cm by 4 cm rectangle to a 5 cm by 3 cm rectangle (with no overlap). What is the total area of the L-shape?
An L-shaped compound shape has the following outer edges, in order: 8 cm, 5 cm, 3 cm, 2 cm, 5 cm, 7 cm. Find its perimeter.
[1 mark]A square of side 10 cm has a circle of radius 4 cm cut out from its centre. Find the remaining area, in terms of pi.
[2 marks]A hollow cylinder (a pipe) has external radius 5 cm and internal radius 3 cm. Its length is 12 cm. Find the volume of the metal in the pipe, in terms of pi.
[2 marks]A semi-circular shape sits on top of a rectangle. The rectangle is 12 cm wide. What is the radius of the semicircle?
A compound shape is formed by a rectangle measuring 14 cm by 8 cm with a semicircle of diameter 8 cm cut out from one of its short ends.
Find the area of the compound shape, in terms of pi.
[2 marks]Find the perimeter of the compound shape, in terms of pi.
[1 mark]A cuboid of dimensions 10 cm by 8 cm by 6 cm has a cone-shaped hole drilled through it. The cone has radius 3 cm and perpendicular height equal to the smallest dimension of the cuboid. Find the remaining volume of the cuboid, in terms of pi.
[2 marks]A frustum is made by removing a small cone from a larger cone. The large cone has radius 10 cm and height 24 cm. The small cone (cut from the top) has radius 4 cm and height 9.6 cm. Find the volume of the frustum, in terms of pi.
[2 marks]Everything students ask about Cambridge IGCSE 0580 Compound shapes and parts of shapes Topical Past Papers.
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