Year 8 - Maths
Finding a length in composite shapes
Perimeter, area and volume
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils extend their knowledge of shapes by exploring the properties of circles and composite shapes before developing understanding of 3-D shapes including surface area and volume.
Lesson Summary
You will learn to solve area problems of composite shapes involving whole and/or part circles where the area is known and the radius or diameter must be found.
Key Notes
- The diameter can be found from the area of circles or parts of circles by rearranging the formula.
- The radius can be found from the area of circles or parts of circles.
- The diameter or radius can be found from the area of composite shapes by reasoning and rearranging the formula.
Vocabulary To Learn
- sector: A sector is the region formed between two radii and their connecting arc.
- diameter: The diameter of a circle is any line segment that starts and ends on the edge of the circle and passes through the centre of the circle.
- radius: The radius is any line segment that joins the centre of a circle to its edge.
Common Mistakes To Avoid
- If I want to find the radius of a semicircle from its area, I halve the area first.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The diameter can be found from the area of circles or parts of circles by rearranging the formula. The radius can be found from the area of circles or parts of circles.
2. Use this key word in a maths sentence and explain it clearly. 'sector'
A sector is the region formed between two radii and their connecting arc. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: If I want to find the radius of a semicircle from its area, I halve the area first. Correction: You must double the area. This calculates the area of a full circle, whose radius can be found by first dividing by π, then square rooting.
More Lessons In This Unit
- Area of a circle Study Guide
- Area of composite shapes Study Guide
- Checking understanding of area Study Guide
- Checking understanding of perimeter Study Guide
- Circumference of a circle Study Guide
- Multiplicative relationships in circles Study Guide
- Perimeter of composite shapes Study Guide
- Problem solving with perimeter, area and volume Study Guide
- Properties of prisms Study Guide
- Surface area of cuboids Study Guide
- Surface area of cylinders Study Guide
- Surface area of prisms Study Guide
- Using the formula for the area of a circle Study Guide
- Volume of cylinders Study Guide
- Volume of prisms Study Guide
Browse all guides in the Year 8 Maths guide library.