Non-right-angled: Challenge & Extension
Mathematics
Grade 7
12 questions
~24 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the area of non-right-angled triangles using the formula ½abSinC, including practice, problem solving, real-world applications, and extension challenges.
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Full preview • 12 questions
Non-right-angled: Challenge & Extension
Subject: MathematicsGrade: Grade 7
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Untitled Worksheet
Grade Grade 7
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the area of a triangle with sides a = 8 cm, b = 6 cm, and the included angle C = 60°.
[3 marks]2.
Given sides a = 10 cm, b = 7 cm, and angle C = 45°, find the area of the triangle.
[3 marks]3.
A triangle has sides a = 5 cm, b = 9 cm, and angle C = 120°. Calculate its area.
[3 marks]4.
Construct a triangle with sides a = 7 cm, b = 9 cm, and angle C = 80°. Use the grid to depict the triangle.
[2 marks]5.
Plot the graph of y=2x and identify a point where a triangle with sides a=5, b=12 and angle C=60° can be constructed.
[2 marks]B
Problem Solving & Reasoning
Solve these multi-step problems. Show detailed working.
1.
A triangle has sides a = 8 cm, b = 10 cm, and included angle C = 75°. Calculate its area and explain each step.
[4 marks]2.
Two sides of a triangle are 6 cm and 9 cm, with an included angle of 100°. Find the area, then determine if this shape can be a potential triangle with the given measurements.
[4 marks]C
Real-world Applications
Interpret the problem and calculate the required area.
1.
A park has two paths that form a triangle with sides 50 m and 70 m, and the included angle is 40°. Find the area of the park section enclosed by the paths.
[3 marks]D
Challenge & Extension
Attempt these advanced problems to deepen your understanding.
1.
Given a triangle with sides a=9 cm, b=12 cm, and area = 54 cm², find the measure of angle C using the Law of Sines and the area formula.
[3 marks]2.
A triangle has sides a=13 cm, b=14 cm, and area = 84 cm². Use the formula ½abSinC to find angle C, and verify your result with the Law of Cosines.
[4 marks]E
Mixed Review & Error Analysis
Identify the errors in the following student solutions and correct them.
1.
A student calculates the area with sides a=8 cm, b=5 cm, and angle C=90°, using the formula ½abSinC. Is this correct? If not, explain and correct the mistake.
[2 marks]2.
A solution shows using sides a=7, b=9, and angle C=60°, but mistakenly uses sin60° = 0.6 instead of 0.866. Identify and correct the mistake.
[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