Length
3.0 Measurements · 3.2 Length
Syllabus tag: Kenya CBC | Grade 7 Mathematics | Strand 3.0 Measurements | Sub-Strand 3.2 Length (6 lessons)
Lesson objectives
By the end of this topic, you will be able to:
- Convert units of length involving cm, dm, m, Dm and Hm
- Perform operations involving units of length
- Work out the perimeter of plane figures
- Work out the circumference of circles
Length
Length measures distance. This topic converts between units and finds the distance round the edge of a shape.
a) The units
| Unit | Short | In metres |
|---|---|---|
| Hectometre | Hm | 100 |
| Decametre | Dm | 10 |
| Metre | m | 1 |
| Decimetre | dm | 0.1 |
| Centimetre | cm | 0.01 |
Each step is ten times the one below it.
Going down the ladder, multiply by 10 each step. Going up, divide by 10.
To convert 3 Hm to metres, that is two steps down, so multiply by 100. The answer is 300 m.
A check: the smaller the unit, the bigger the number. If converting metres to centimetres gives a smaller number, you went the wrong way.
b) Operations with lengths
Convert everything to the same unit before adding or subtracting. You cannot add 3 m to 40 cm as they stand.
Change 3 m to 300 cm, then add to get 340 cm. Or change 40 cm to 0.4 m and get 3.4 m. Either is right, as long as you say which unit the answer is in.
c) Perimeter
The perimeter is the distance all the way round a flat shape.
For any shape with straight sides, add up every side.
For a rectangle there is a shortcut, since opposite sides are equal: perimeter = 2(l + w).
For a square, all four sides are equal, so perimeter = 4 × side.
Work inside the bracket first. Doubling 9 and then adding 5 gives 23, which is wrong.
d) Circumference
The circumference is the perimeter of a circle.
The rule is C = 2πr, where r is the radius.
Use 22/7 for π when the radius is a multiple of 7, since the sevens cancel.
If the question gives the diameter, halve it first to get the radius. Using the diameter as the radius doubles the answer.
e) Perimeter of combined shapes
Some shapes mix straight and curved parts. A rectangle with a semicircle on one end is a common example.
Work out each part separately, then add only the edges that are actually on the outside.
The straight edge where the two shapes join sits inside the figure. It is not part of the perimeter.
f) Where this is used
Fencing a plot. Edging a table. Working out how much ribbon goes round a cake. Measuring cloth for a hem.
Words to know
- Perimeter — the total distance around a straight-sided shape.
- Circumference — the total distance around a circle.
- π (pi) — the constant ratio between a circle's circumference and its diameter, approximately 3.14 or 22/7.
- Diameter — the distance across a circle through its centre.
- Radius — the distance from a circle's centre to its edge, half the diameter.
:::checkpoint Check yourself
- Convert 4 Dm into centimetres.
- Find the perimeter of a rectangle 12 cm by 7 cm.
- Find the circumference of a circle of radius 14 cm, taking π as 22/7.
- Why must units be the same before you add two lengths? :::
Bridge to practice
Try the exercises below — on length conversion, perimeter and circumference.