Primary 6 maths · Geometry · About 12 minutes
Find areas and perimeters of semicircles and quarter-circles
Mark the centre, radius and required outer boundary or surface before calculating.
Start the interactive lesson →Open practice activity
What you will learn
- Find areas and perimeters of semicircles and quarter-circles
Models used: number sentences, stories, diagrams.
Before you start
The curved edge is not the whole perimeter
A semicircle contains half of the full circle’s area.
A semicircle contains half of the full circle’s area.
area = π × 7² ÷ 2
A diameter contains two radii. A partial-circle perimeter may also contain straight edges; its area concerns the enclosed surface.
A semicircle of radius seven centimetres. Its curved edge is half the full circumference: 22 cm when π = 22/7.
arc = 2 × (22/7) × 7 ÷ 2 = 22 cm
Trace the curved edge. To walk all the way around, you must also walk the straight diameter, 14 cm.
perimeter = 22 + 14 = 36 cm
The straight edge belongs to the outer boundary too. For a quarter-circle, use a quarter of the arc and add its two radii.
perimeter = 11 + 7 + 7 = 25 cm
The boundary includes two radii and one quarter of the circle.
What did the picture help us see?
For a quarter-circle, use a quarter of the arc and add its two radii.
Worked example: A new example, together
Find the perimeter of a semicircle with radius 14 cm. Use π = 22/7.
Mark the centre, radius and required outer boundary or surface before calculating.
A perimeter includes every part of the outer boundary, curved or straight.
The radius is half the diameter. The radius is 14 cm; diameter is 28 cm.
The radius is half the diameter. Find the perimeter of a semicircle with radius 14 cm. Use π = 22/7.
72 cm
The radius is 14 cm; diameter is 28 cm.
The radius is half the diameter. Curved length = 2 × (22/7) × 14 ÷ 2.
The radius is half the diameter. Include the straight edges (28 cm): total 72 cm.
The radius is half the diameter. Check the result against the question we started with.
Trace all curved and straight outer edges once.
We found 72 cm. A perimeter includes every part of the outer boundary, curved or straight.
The radius is half the diameter.
Common mistakes to discuss
- Forgetting the straight edge. Half a circle’s perimeter is half the circumference plus the diameter; a quarter needs its two radii.
Check your understanding
- Find areas and perimeters of semicircles and quarter-circles
- 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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