Trapezium: Error Analysis & Misconceptions
Mathematics
Grade 8
10 questions
~20 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the properties of trapeziums, focusing on common errors and misconceptions through calculations, reasoning, and real-world applications.
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Trapezium: Error Analysis & Misconceptions
Subject: MathematicsGrade: Grade 8
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Untitled Worksheet
Grade Grade 8
A
Fluency & Practice
Solve the following questions involving basic properties and calculations related to trapeziums. Show all working.
1.
Calculate the length of the shorter parallel side in a trapezium where the longer parallel side is 12 cm, the non-parallel sides are both 8 cm, and the height is 6 cm.
[3 marks]2.
If the bases of a trapezium are 10 cm and 16 cm and the height is 5 cm, find the area of the trapezium.
[3 marks]3.
In a trapezium, the lengths of the bases are 9 cm and 15 cm. The non-parallel sides are equal, each measuring 7 cm. Find the measure of the angles adjacent to the longer base.
[4 marks]B
Problem Solving & Reasoning
Answer these multi-step questions and explain your reasoning clearly.
1.
A trapezium has bases of 8 cm and 14 cm, and the height is 5 cm. The non-parallel sides are 6 cm each. Determine whether the trapezium is isosceles and justify your answer.
[4 marks]2.
A trapezium has an area of 48 cm², with bases measuring 12 cm and 8 cm. Find its height and explain each step.
[4 marks]C
Real-world Applications
Apply your understanding of trapeziums to solve these contextual problems.
1.
A trapezoidal swimming pool has parallel sides measuring 20 m and 30 m, with a uniform depth of 2 m. If the sides are sloped and each non-parallel side measures 25 m, find the total volume of water the pool can hold.
[4 marks]D
Challenge & Extension
Tackle these advanced problems that extend your understanding of trapeziums.
1.
Construct a trapezium where the longer base is 10 cm, the shorter base is 6 cm, and the non-parallel sides are both 5 cm. Verify whether the trapezium is isosceles. Show all your construction steps.
[4 marks]2.
Derive a formula to find the length of the non-parallel sides of a trapezium given the lengths of the bases and the height, and verify it with an example where bases are 9 cm and 15 cm, and height is 4 cm.
[4 marks]E
Mixed Review & Common Misconceptions
Identify errors in the following statements or calculations related to trapeziums.
1.
A student states: "In a trapezium, only the bases are parallel, and the non-parallel sides can be unequal." Is this statement always true? Explain your answer.
[3 marks]2.
A calculation shows a trapezium with bases 8 cm and 12 cm, and height 4 cm. The student claims the area is 40 cm². Identify and correct the mistake.
[3 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet