½ × b × h: Challenge & Extension
Mathematics
Year 9
12 questions
~24 mins
1 views0 downloads
About This Worksheet
A challenging worksheet focusing on calculating the area of triangles using the formula ½ × b × h, including procedural practice, reasoning, real-world applications, and extension questions.
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½ × b × h: Challenge & Extension
Subject: MathematicsGrade: Year 9
Name:
Date:
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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 triangle with a base of 10 cm and a height of 6 cm.
[2 marks]2.
A triangle has a base of 15 m and an area of 45 m². Find its height.
[3 marks]3.
Construct a triangle on the grid with a base of 8 units and a height of 5 units. Calculate its area.
[3 marks]4.
Calculate the area of a triangle with base 12 cm and height 9 cm.
[2 marks]B
Problem Solving & Reasoning
Answer the following multi-step questions, explaining your reasoning.
1.
A triangular garden has a perimeter of 30 meters. Its base is 10 meters. If the height is twice the length of the base, find the area of the garden.
[4 marks]2.
A ladder leans against a wall, forming a right triangle. The ladder is 15 meters long, and the foot of the ladder is 9 meters from the wall. Calculate the height at which the ladder touches the wall, then find the area of the triangle formed.
[4 marks]C
Real-world Applications
Solve these problems based on real-world contexts.
1.
A carpenter is designing a triangular window frame with a base of 4 meters and a height of 3 meters. What is the area of the window opening?
[2 marks]2.
A triangular plot of land has a base of 25 meters and an area of 150 m². What is the height of the land?
[3 marks]D
Challenge & Extension
Attempt these challenging problems to extend your understanding.
1.
A triangle has a base of 20 cm and a height of 8 cm. If the height is increased by 50%, what is the new area?
[3 marks]2.
Design a triangle on the grid with a base of 7 units and a height of 4 units. Calculate its area and explain how changing the height to 6 units affects the area.
[4 marks]E
Mixed Review & Error Analysis
Answer these questions and identify common mistakes.
1.
A student calculates the area of a triangle with base 9 cm and height 4 cm as 36 cm². Is this correct? If not, what is the mistake and what is the correct area?
[3 marks]2.
Identify the error in this calculation: base = 14 m, height = 5 m, area = 70 m².
[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.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet