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Mensuration: perimeter and area of plane figures — KCSE Mathematics

KCSE Mathematics · 104 practice questions · 4 syllabus objectives

32 easy34 medium38 hard

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Calculate the perimeter and area of triangles, parallelograms, trapeziums and compound shapes

Calculate the circumference and area of a circle; find arc length and area of a sector using the angle

Apply area formulae to solve problems involving land (in acres and hectares), material and design

Mensuration: perimeter and area of plane figures

Sample Questions

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1
easySHORT ANSWER4 marks

A circular flower bed has a radius of 2 m. Explain how to find: (a) the area of the flower bed in square metres. (b) the circumference of the flower bed in metres. (4 marks)

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Part (a) — 2 marks
Area = π × radius² = π × (2 m)² = 4π m² (1 mk)
Area ≈ 12.57 m² (using π ≈ 3.14) (1 mk)
Part (b) — 2 marks
Circumference = 2π × radius = 2π × 2 m = 4π m (1 mk)
Circumference ≈ 12.57 m (using π ≈ 3.14) (1 mk)
2
easySHORT ANSWER3 marks

A rectangular garden measures 30 m by 40 m. Calculate the area of the garden in square metres and convert this area to hectares. (3 marks)

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Part (a) — 1 mark
Area = length × width = 30 m × 40 m = 1200 m² (1 mk)
Part (b) — 2 marks
Convert area to hectares: 1200 m² ÷ 10000 = 0.12 hectares (2 mks)
3
easySHORT ANSWER3 marks

A sector of a circle has a radius of 10 cm and a central angle of 60°. Calculate the area of the sector. (Take π = 22/7) (3 marks)

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Part (a) — 3 marks
Area formula: A = (angle/360) × πr² (1 mk)
A = (60/360) × 22/7 × 10² (1 mk)
A = (1/6) × 22/7 × 100 = 35.33 cm² (1 mk)
4

A trapezium has parallel sides measuring 10 cm and 6 cm, with a height of 4 cm. State the area of the trapezium. (2 marks)

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Why Practise Mensuration: perimeter and area of plane figures?

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Master Mensuration: perimeter and area of plane figures for KCSE

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