Non-right-angled: Mixed Review
Mathematics
Grade 8
12 questions
~24 mins
1 views0 downloads
About This Worksheet
A worksheet covering the area of non-right-angled triangles using the formula ½abSinC, with a variety of question types including practice, reasoning, real-world applications, and challenging problems.
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Full preview • 12 questions
Non-right-angled: Mixed Review
Subject: MathematicsGrade: Grade 8
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Untitled Worksheet
Grade Grade 8
A
Fluency & Practice
Calculate the area of each triangle using the given sides and included angles. Show all working in the grid spaces provided.
1.
Sides a = 8 cm, b = 10 cm, and included angle C = 60°. Calculate the area of the triangle.
[3 marks]2.
Sides a = 5 m, b = 7 m, and included angle C = 45°. Find the area.
[3 marks]3.
Sides a = 12 cm, b = 9 cm, and included angle C = 30°. Calculate the area.
[3 marks]4.
Sides a = 6 ft, b = 8 ft, and included angle C = 90°. Find the area.
[3 marks]B
Problem Solving & Reasoning
Work through these multi-step problems carefully. Explain your reasoning where appropriate.
1.
A triangle has sides a = 7 cm, b = 9 cm, and the included angle C = 120°. Calculate its area. Then, explain how changing angle C to 90° would affect the area.
[4 marks]2.
Find the area of a triangle where side a = 10 m, side b = 14 m, and the included angle C is 75°. If the angle is mistakenly taken as 105°, what error does this cause in the area calculation?
[4 marks]C
Real-world Applications
Apply the area formula to these practical scenarios.
1.
A farmer is designing a triangular plot of land. Two sides measure 50 m and 80 m, with an included angle of 60°. Calculate the area to estimate the land size.
[4 marks]2.
A surveyor needs to find the area of a triangular section of land. The sides are 120 ft and 150 ft, with an included angle of 45°. Calculate the area for accurate mapping.
[4 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 the included angle C.
[4 marks]2.
Construct a triangle with sides 7 cm, 10 cm, and 12 cm. Using the grid, approximate the included angle C and then find the area.
[4 marks]E
Error Analysis
Identify and correct the common mistake in these problems.
1.
A student calculates the area of a triangle using sides a=8, b=6, and angle C=60° but gets 48. Identify the mistake and provide the correct calculation.
[4 marks]2.
A student assumes the area is maximized at 180° instead of 90°. Explain why this is incorrect and what the maximum angle should be for maximum area.
[4 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