Grade 10 Perimeter: Short Notes

10 ශ්‍රේණිය · 1 වාරය · 1 පරිච්ඡේදය · පරිමිතිය

96%

of Grade 10 term tests include it (52 of 54)

534

marks in past papers (99 questions)

10 min

full lesson with quick checks

🎯 What you'll learn

Name the parts of a sector: centre, radii, arc and centre angle
Find the arc length of a sector using θ/360 × 2πr
Find the perimeter of a sector, a semicircle and a quadrant
Find the perimeter of compound figures that contain sectors
Work backwards from a perimeter to find the radius

Light up the stage

Your school's prize-giving stage sits in a corner of the hall and is shaped like a quarter of a circle. The teacher asks how many metres of LED strip will run right round its edge. The two straight edges are easy to measure. But how long is the curved edge? That's this lesson.

Quick recap

Perimeter is the total length around the edge of a shape.The perimeter of a whole circle is its circumference:C = 2πr (r = radius)In term tests we usually take π = 22/7, so radii like 7, 14 and 21 cancel nicely with the 7.Remember: diameter = 2 × radius.

Parts of a sector

A sector is the part of a circle bounded by two radii and the arc between them, like a slice of a round cake. The amber curve is the arc (length l); θ is the centre angle.

An arc is a fraction of a circle

A full turn is 360°. A sector with centre angle θ is θ/360 of the whole circle, so its arc is θ/360 of the circumference.• 180° → ½ (semicircle)• 90° → ¼ (quadrant)• 60° → 1/6• 45° → 1/8• 120° → 1/3

🧮 Arc length

Use it whenever you need the length of a curved edge. l is the arc length, θ the centre angle in degrees and r the radius.

l = θ/360 × 2πr

✏️ Arc of a 60° sector

A sector has radius 21 cm and centre angle 60°. Find the length of its arc.

160° is 60/360 = 1/6 of a full turn.
2Circumference = 2 × 22/7 × 21 = 132 cm.
3Arc = 1/6 × 132 = 22 cm.

✅ 22 cm

🧮 Perimeter of a sector

Walk round the edge: one radius, the arc, then the other radius back to the centre.Semicircle: P = πr + 2rQuadrant: P = πr/2 + 2r

P = 2r + θ/360 × 2πr

✏️ The quarter-circle stage

Back to the stage: it is a quadrant of radius 14 m. How much LED strip goes right round its edge?

1A quadrant has a 90° angle, so its arc is ¼ of the circumference.
2Arc = ¼ × 2 × 22/7 × 14 = 22 m.
3Add the two straight edges (radii): 14 + 14 = 28 m.
4Perimeter = 22 + 28 = 50 m.

✅ 50 m

⚠️ The arc alone is not the perimeter

Two slips cost marks every year:1. Writing only the arc. A sector's perimeter also includes its two radii (for a semicircle, the diameter).2. Using the diameter as the radius. In past O/L papers about a quarter of candidates forgot to halve it.Always write r = ... before you start.

Compound figures: trace the outside

A compound figure joins sectors to rectangles, squares or triangles.1. Trace the outside edge once with your finger.2. List each piece you pass: straight sides and arcs.3. Find each arc with θ/360 × 2πr.4. Add them up.A line inside the figure, where two shapes join, is not part of the perimeter.

⚠️ Don't count the hidden side

A common exam error: finding the whole perimeter of the rectangle and of the semicircle, then adding them. That counts the joining line twice, when it shouldn't be counted at all. For the card above, 48 + 36 = 84 cm is wrong. Only edges you could walk along from outside count.

📌 Remember

• Arc length = θ/360 × 2πr (take π = 22/7).• Perimeter of a sector = arc + 2 radii.• Semicircle: πr + 2r. Quadrant: πr/2 + 2r.• If the diameter is given, halve it first.• Compound figure: trace the outside only; inner joining lines don't count.

🧾 Quick revision sheet

What is a sector?	The part of a circle bounded by two radii and the arc between them.
Arc length of a sector (angle θ, radius r)	θ/360 × 2πr
Perimeter of a sector	Two radii + arc = 2r + θ/360 × 2πr
Perimeter of a semicircle of radius r	πr + 2r
Arc of a quadrant of radius r	πr/2 (a quarter of 2πr)
What fraction of a circle is a 60°, 45° or 120° sector?	1/6, 1/8 and 1/3
Arc of a 90° sector with r = 14 cm	22 cm (¼ × 2 × 22/7 × 14)
Perimeter of a compound figure	Add only the outside edges; leave out lines where shapes join.