Geometry: quadrilaterals and polygons — KCSE Mathematics

KCSE Mathematics · 97 practice questions · 4 syllabus objectives

36 easy34 medium27 hard

What You'll Learn

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

Identify and state the properties of quadrilaterals (parallelogram, rectangle, rhombus, square, trapezium, kite)

Calculate the sum of interior and exterior angles of any polygon and the size of each angle of a regular polygon

Solve problems involving the area of quadrilaterals and polygons using appropriate formulae

Geometry: quadrilaterals and polygons

Sample Questions

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1
easySHORT ANSWER2 marks

A rhombus has diagonals measuring 8 cm and 6 cm. Find the area of the rhombus. (2 marks)

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Part (a) — 2 marks
Area = ½ × diagonal1 × diagonal2 = ½ × 8 cm × 6 cm (1 mk)
State the area = 24 cm² (1 mk)
2
easySHORT ANSWER2 marks

In a rectangle, the length is 10 cm and the width is 5 cm. Calculate the area of the rectangle. (2 marks)

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Part (a) — 2 marks
Area = length × width = 10 cm × 5 cm (1 mk)
State the area = 50 cm² (1 mk)
3
easySHORT ANSWER4 marks

Each exterior angle of a regular polygon measures 45°. (a) Find the number of sides of the polygon. (b) Calculate the sum of all interior angles of the polygon. (4 marks)

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Part (a) — 2 marks
Use the formula n = 360/45 (1 mk)
State n = 8 (1 mk)
Part (b) — 2 marks
Sum of interior angles = (n − 2) × 180 = (8 − 2) × 180 (1 mk)
Sum of interior angles = 1080° (1 mk)
4

A regular polygon has a sum of interior angles equal to 720°. (a) Determine the number of sides of the polygon. (b) Calculate the measure of each interior angle. (4 marks)

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KNEC Aligned

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