Primary 6 maths · Geometry · About 12 minutes
Solve composite-circle area and perimeter problems
Mark the centre, radius and required outer boundary or surface before calculating.
Start the interactive lesson →Open practice activity
What you will learn
- Solve composite-circle area and perimeter problems
Models used: number sentences, stories, tables.
Before you start
From the centre, across, and around
A radius reaches from the centre to the edge.
The centre is the middle point. A radius joins it to the edge; a diameter passes through it.
A radius reaches from the centre to the edge.
The centre is the middle point. A radius joins it to the edge; a diameter passes through it.
A diameter crosses the centre. It is two radii long.
diameter = 2 × radius
The centre is the middle point. A radius joins it to the edge; a diameter passes through it.
Circumference measures the path all the way around the edge.
circumference = π × diameter
What did the picture help us see?
Circumference measures the path all the way around the edge.
Worked example: A new example, together
A rectangle 28 cm wide and 7 cm high has a semicircle of diameter 28 cm on top. Find the total area. Use π = 22/7.
| Rectangle width | Rectangle height | Semicircle diameter |
|---|---|---|
| 28 | 7 | 28 |
The semicircle diameter is the shared internal edge. Read each value with the heading above its column.
Mark the centre, radius and required outer boundary or surface before calculating.
Circular area scales with the square of the radius and the fraction of the circle used.
The semicircle diameter is the shared internal edge. Rectangle width Rectangle height Semicircle diameter 28 7 28 The semicircle diameter is the shared internal edge. Read each value with the heading above its column.
The semicircle radius is 14 cm.
The semicircle diameter is the shared internal edge. Rectangle width Rectangle height Semicircle diameter 28 7 28 A rectangle 28 cm wide and 7 cm high has a semicircle of diameter 28 cm on top. Find the total area. Use π = 22/7.
504 cm²
The semicircle diameter is the shared internal edge. Read each value with the heading above its column.
Area: rectangle + half of a circle.
The semicircle diameter is the shared internal edge. Rectangle width Rectangle height Semicircle diameter 28 7 28 The semicircle diameter is the shared internal edge. Read each value with the heading above its column.
28 × 7 + (22/7) × 14² ÷ 2 = 504 cm².
The semicircle diameter is the shared internal edge. Rectangle width Rectangle height Semicircle diameter 28 7 28 The semicircle diameter is the shared internal edge. Read each value with the heading above its column.
Check the result against the question we started with.
The shared diameter is inside the figure, so it is not counted in the outer perimeter.
We found 504 cm². Circular area scales with the square of the radius and the fraction of the circle used.
The semicircle diameter is the shared internal edge. Rectangle width Rectangle height Semicircle diameter 28 7 28
Common mistakes to discuss
- Counting a hidden edge. Where shapes join, the shared edge is inside the figure and is not part of its perimeter.
Check your understanding
- Solve composite-circle area and perimeter problems
- justify circle calculations using the correct radius and region
- check the answer against the original quantities and units
Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.
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