½(a+b)h: Real-world Applications in Engineering
Mathematics
Year 9
14 questions
~28 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on the formula ½(a+b)h for calculating the area of trapeziums, with applications in engineering contexts. Includes practice, problem solving, and extension questions.
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½(a+b)h: Real-world Applications in Engineering
Subject: MathematicsGrade: Year 9
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Untitled Worksheet
Grade Year 9
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the area of a trapezium with parallel sides measuring 8 cm and 12 cm, and a height of 5 cm.
[2 marks]2.
A trapezium has bases of 10 cm and 14 cm, and the height is 6 cm. Find its area.
[2 marks]3.
Determine the area of a trapezium with a height of 4 m, and bases measuring 9 m and 15 m.
[2 marks]4.
A trapezium has a longer base of 20 m, a shorter base of 12 m, and an area of 144 m². Find the height.
[3 marks]B
Problem Solving & Reasoning
Solve the following multi-step problems and explain your reasoning clearly.
1.
An engineer is designing a trapezoidal support beam with bases of 5 m and 9 m, and a height of 3 m. If the support needs to be reinforced with additional material to increase its area to 24 m², what should be the new height if the bases remain the same?
[4 marks]2.
A bridge has a trapezoidal cross-section with bases of 4 m and 7 m, and a height of 2.5 m. If the total area of all cross-sections along 50 meters is 162.5 m², verify this total area using the formula.
[4 marks]C
Real-world Applications
Answer these context-based questions related to engineering projects.
1.
An architect is designing a trapezoidal window frame. The top base measures 1.2 meters, the bottom base 1.8 meters, and the height is 0.75 meters. Calculate the total area of the window frame.
[3 marks]2.
A factory machine supports a trapezoidal platform with bases of 2.5 m and 3.5 m, and a height of 0.8 m. If the total platform area needs to be 5.6 m², what should be the height?
[3 marks]D
Challenge & Extension
Attempt these advanced questions to extend your understanding.
1.
A trapezium is part of a larger engineering structure. If the area of the trapezium is 36 m², the shorter base is 4 m, and the longer base is 8 m, find the height. Then, verify whether doubling the height results in an area of 72 m².
[4 marks]2.
Design a trapezium with bases in ratio 1:2, height of 3 m, and area of 18 m². What are the lengths of the bases?
[4 marks]E
Mixed Review
Answer these questions to review your understanding of ½(a+b)h.
1.
A trapezium has bases of 7 cm and 11 cm, and a height of 4 cm. Calculate its area.
[2 marks]2.
Construct a trapezium on the grid with bases measuring 5 cm and 9 cm, and height 3 cm. Calculate its area.
[2 marks]F
Error Analysis
Review these common mistakes and identify the errors.
1.
A student calculates the area of a trapezium with bases 6 m and 10 m, and height 4 m, using the formula ½(a×b)h. The answer given is 32 m². Identify and correct the mistake.
[2 marks]2.
A student forgets to add the bases before multiplying by height, calculating area as ½(6×10)×4 = 120. What's wrong with this calculation?
[2 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet