PSLE Circles: Complete Guide to Circumference, Area & Composite Figures

Circle problems are PSLE favourites worth 3-5 marks each! Master the formulas, learn when to use π = 3.14 vs 22/7, and conquer semicircles, quarter circles, and composite figures.

Why Circles Are Essential for PSLE

Circle questions appear in almost every PSLE Math paper. They test your understanding of:

Circumference (the distance around a circle)
Area (the space inside a circle)
Partial circles (semicircles and quarter circles)
Composite figures (combining circles with other shapes)

The good news? Once you master the core formulas and know when to use each value of π, these problems become very manageable!

The Essential Formulas

Circumference

$C = 2 \times \pi \times r$ $\text{or } C = \pi \times d$

Distance around the circle

Area

$A = \pi \times r \times r$ $\text{or } A = \pi r^2$

Space inside the circle

Radius & Diameter Relationship:

$d = 2 \times r \quad \text{and} \quad r = d \div 2$

The diameter is always twice the radius!

Understanding Pi (π)

Pi (π) is a special number that equals approximately 3.14159… In PSLE, you’ll use one of two values:

π = 3.14

Use when the question says “Take π = 3.14”

Good for any radius or diameter

π = 22/7

Use when the question says “Take π = 22/7”

Best when radius/diameter is a multiple of 7

💡 When to Use 22/7

Look for multiples of 7 in the radius or diameter: 7, 14, 21, 28, 35… The 7 in the denominator cancels out, making calculations easier!

Interactive Circle Calculator

Use this calculator to check your working and see step-by-step solutions:

Circle Properties Calculator

What do you know?

Value of π (as specified in question)

Enter Radius (r)

Part 1: Circumference (C = πd or C = 2πr)

The circumference is the distance around a circle - like its perimeter!

Example 1: Circumference from Diameter

Problem:

Find the circumference of a circle with diameter 14 cm. (Take π = 22/7)

Circumference = π × diameter
Circumference = 22/7 × 14
Circumference = 22 × 2 = 44 cm

💡 Notice the 7s Cancel!

14 ÷ 7 = 2, so 22/7 × 14 = 22 × 2 = 44. That’s why 22/7 works beautifully with multiples of 7!

Example 2: Circumference from Radius

Problem:

A circular track has radius 35 m. How far does an athlete run in one lap? (Take π = 22/7)

One lap = circumference
Circumference = 2 × π × r
Circumference = 2 × 22/7 × 35
Circumference = 2 × 22 × 5 = 220 m

Example 3: Using π = 3.14

Problem:

A circular plate has diameter 20 cm. Find its circumference. (Take π = 3.14)

Circumference = π × diameter
Circumference = 3.14 × 20
Circumference = 62.8 cm

Part 2: Area (A = πr²)

Area is the space INSIDE the circle. Always use the radius (not diameter) in the formula!

⚠️ Critical Reminder

Area uses RADIUS, not diameter! If you’re given the diameter, find the radius first by dividing by 2.

Example 4: Area from Radius

Problem:

Find the area of a circle with radius 7 cm. (Take π = 22/7)

Area = π × r × r
Area = 22/7 × 7 × 7
Area = 22 × 7 = 154 cm²

Example 5: Area from Diameter

Problem:

A circular pond has diameter 20 m. Find its area. (Take π = 3.14)

Step 1: Find radius
Radius = 20 ÷ 2 = 10 m
Step 2: Find area
Area = 3.14 × 10 × 10 = 314 m²

Part 3: Semicircles (Half Circles)

A semicircle is exactly half of a circle. The tricky part is finding its perimeter!

Semicircle Area

$\text{Area} = \frac{1}{2} \times \pi \times r^2$

Half the full circle area

Semicircle Perimeter

$\text{Perimeter} = \text{Arc} + \text{Diameter}$

Arc = half the circumference

Example 6: Perimeter of a Semicircle

Problem:

Find the perimeter of a semicircle with diameter 14 cm. (Take π = 22/7)

Step 1: Find the arc (curved part)
Arc = 1/2 × π × d = 1/2 × 22/7 × 14 = 22 cm
Step 2: Add the diameter (straight part)
Perimeter = Arc + Diameter = 22 + 14 = 36 cm

⚠️ Don't Forget the Diameter!

The perimeter of a semicircle has TWO parts: the curved arc AND the straight diameter!

Example 7: Area of a Semicircle

Problem:

Find the area of a semicircle with radius 14 m. (Take π = 22/7)

Area of full circle = 22/7 × 14 × 14 = 616 m²
Area of semicircle = 616 ÷ 2 = 308 m²

Part 4: Quarter Circles

A quarter circle is one-fourth of a circle. Think of it as a “corner” shape.

Quarter Circle Area

$\text{Area} = \frac{1}{4} \times \pi \times r^2$

One-fourth of full circle area

Quarter Circle Perimeter

$\text{Perimeter} = \text{Arc} + r + r$

Arc = 1/4 of circumference

Example 8: Perimeter of a Quarter Circle

Problem:

Find the perimeter of a quarter circle with radius 7 cm. (Take π = 22/7)

Step 1: Find the arc
Arc = 1/4 × 2 × π × r = 1/4 × 2 × 22/7 × 7 = 11 cm
Step 2: Add both radii (two straight edges)
Perimeter = Arc + r + r = 11 + 7 + 7 = 25 cm

Example 9: Area of a Quarter Circle

Problem:

Find the area of a quarter circle with radius 10 cm. (Take π = 3.14)

Area of full circle = 3.14 × 10 × 10 = 314 cm²
Area of quarter circle = 314 ÷ 4 = 78.5 cm²

Part 5: Three-Quarter Circles

A three-quarter circle is 3/4 of a circle - imagine a circle with a quarter “bitten out”!

Example 10: Perimeter of a Three-Quarter Circle

Problem:

Find the perimeter of a three-quarter circle with radius 14 cm. (Take π = 22/7)

Step 1: Find the arc (3/4 of circumference)
Arc = 3/4 × 2 × π × r = 3/4 × 2 × 22/7 × 14
Arc = 3/4 × 88 = 66 cm
Step 2: Add both radii
Perimeter = 66 + 14 + 14 = 94 cm

Part 6: Composite Figures

Composite figures combine circles (or parts of circles) with other shapes like rectangles. There are two main methods:

Addition Method

Shapes are JOINED together

Total Area = Shape A + Shape B

Subtraction Method

Shape is CUT OUT from another

Shaded Area = Big Shape - Cutout

Example 11: Stadium Shape (Addition)

Problem:

A playground is made of a rectangle (50 m × 20 m) with two semicircles on the shorter ends. Find the area. (Take π = 3.14)

Step 1: Identify the shapes
Rectangle: 50 m × 20 m
Two semicircles with diameter 20 m (radius = 10 m)
Step 2: Area of rectangle = 50 × 20 = 1000 m²
Step 3: Two semicircles = one full circle
Area of circle = 3.14 × 10 × 10 = 314 m²
Step 4: Total area = 1000 + 314 = 1314 m²

💡 Shortcut: 2 Semicircles = 1 Circle

When you have two semicircles with the same radius, just calculate one full circle!

Example 12: Corner Cut-Out (Subtraction)

Problem:

A square tile has side 10 cm. A quarter circle is cut from one corner. Find the shaded area. (Take π = 3.14)

Area of square = 10 × 10 = 100 cm²
Area of quarter circle = 1/4 × 3.14 × 10 × 10 = 78.5 cm²
Shaded area = 100 - 78.5 = 21.5 cm²

Example 13: Decorative Ring

Problem:

A ring is made from two circles. The outer circle has radius 20 cm and the inner circle has radius 10 cm. Find the area of the ring. (Take π = 3.14)

Area of outer circle = 3.14 × 20 × 20 = 1256 cm²
Area of inner circle = 3.14 × 10 × 10 = 314 cm²
Area of ring = 1256 - 314 = 942 cm²

Common Mistakes to Avoid

❌ Mistake 1: Using Diameter for Area

Area = π × r × r, NOT π × d × d! Always find the radius first.

❌ Mistake 2: Forgetting Part of the Perimeter

Semicircle perimeter = Arc + Diameter (2 parts)
Quarter circle perimeter = Arc + r + r (3 parts)

❌ Mistake 3: Wrong Value of π

Always use the value specified in the question! Don’t mix 3.14 and 22/7.

❌ Mistake 4: Forgetting cm² for Area

Circumference/Perimeter uses cm (linear), Area uses cm² (squared)!

Quick Reference Table

Shape	Perimeter/Circumference	Area
Full Circle	C = 2πr = πd	A = πr²
Semicircle	P = 1/2 × πd + d	A = 1/2 × πr²
Quarter Circle	P = 1/4 × 2πr + 2r	A = 1/4 × πr²
Three-Quarter Circle	P = 3/4 × 2πr + 2r	A = 3/4 × πr²

PSLE-Style Challenge Problems

Challenge 1:

A rectangular plot measures 42 m by 28 m. A semicircle with diameter 28 m is attached to one of the shorter sides. Find:

(a) The perimeter of the whole plot

(b) The area of the whole plot (Take π = 22/7)

Click to reveal solution

Part (a): Perimeter

Perimeter = 2 long sides + 1 short side + semicircle arc

= 2 × 42 + 28 + 1/2 × π × 28

= 84 + 28 + 1/2 × 22/7 × 28

= 112 + 44 = 156 m

Part (b): Area

Rectangle area = 42 × 28 = 1176 m²

Semicircle radius = 14 m

Semicircle area = 1/2 × 22/7 × 14 × 14 = 308 m²

Total area = 1176 + 308 = 1484 m²

Challenge 2:

A square has side 14 cm. Four quarter circles, each with radius 7 cm, are cut from the four corners. Find the area of the remaining figure. (Take π = 22/7)

Click to reveal solution

Key insight: 4 quarter circles = 1 full circle!

Area of square = 14 × 14 = 196 cm²

Area of 4 quarters = 22/7 × 7 × 7 = 154 cm²

Remaining area = 196 - 154 = 42 cm²

Key Takeaways

✓ Circumference = 2πr or πd (distance around)
✓ Area = πr² (always use radius, not diameter!)
✓ Semicircle perimeter = arc + diameter (don’t forget the straight edge!)
✓ Quarter circle perimeter = arc + r + r (two straight edges!)
✓ Use 22/7 when radius/diameter is a multiple of 7
✓ 2 semicircles = 1 circle and 4 quarter circles = 1 circle
✓ Composite figures: add when joined, subtract when cut out

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PSLE Circles: Complete Guide to Circumference, Area & Composite Figures

PSLE Circles: Complete Guide to Circumference, Area & Composite Figures

Why Circles Are Essential for PSLE

The Essential Formulas

Understanding Pi (π)

Interactive Circle Calculator

Circle Properties Calculator

Part 1: Circumference (C = πd or C = 2πr)

Part 2: Area (A = πr²)

Part 3: Semicircles (Half Circles)

Part 4: Quarter Circles

Part 5: Three-Quarter Circles

Part 6: Composite Figures

Common Mistakes to Avoid

Quick Reference Table

PSLE-Style Challenge Problems

Key Takeaways

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