Parallelogram: Challenge & Extension
Mathematics
GCSE Foundation
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the properties of parallelograms, including calculations, reasoning, and real-world applications suitable for GCSE Foundation students seeking extension.
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Parallelogram: Challenge & Extension
Subject: MathematicsGrade: GCSE Foundation
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Untitled Worksheet
Grade GCSE Foundation
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
A parallelogram has a base length of 8 cm and a height of 5 cm. Calculate its area.
[2 marks]2.
In a parallelogram, the lengths of sides AB and AD are 10 cm and 6 cm respectively. If the angles are such that the height from AB is 4 cm, find the length of the base AB.
[3 marks]3.
A parallelogram has sides of 7 cm and 9 cm. One of its angles measures 60°. Calculate the height corresponding to the base of 9 cm.
[3 marks]4.
Construct a parallelogram with sides of 6 cm and 8 cm where the angle between the sides of 6 cm and 8 cm is 45°. Show all your construction steps.
[4 marks]5.
Explain why the diagonals of a parallelogram bisect each other. Provide a brief reasoning based on geometric properties.
[3 marks]6.
A parallelogram has diagonals measuring 10 cm and 12 cm, which bisect each other at an angle of 60°. Calculate the area of the parallelogram.
[4 marks]7.
A rectangle is a special case of a parallelogram. If a parallelogram has sides of 8 cm and 15 cm and one angle of 60°, find its area.
[3 marks]8.
A student mistakenly claims that the area of a parallelogram can be found simply by multiplying two adjacent sides. Identify and explain the mistake in this reasoning.
[3 marks]9.
Given a parallelogram with sides 9 cm and 14 cm, and an included angle of 75°, calculate its area.
[4 marks]10.
A large parallelogram has diagonals of 20 cm and 24 cm. The diagonals intersect at an angle of 70°. Use this information to estimate the area.
[4 marks]11.
Challenge: Derive the formula for the area of a parallelogram using the lengths of its diagonals and the angle between them.
[5 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet