Estimating and measuring area and perimeter
🎯 In this topic you will
- Estimate and measure the perimeter of two-dimensional shapes.
- Use millimetres (mm), centimetres (cm), metres (m), and kilometres (km) to record perimeter.
- Record area using square units including mm², cm², m², and km².
- Estimate the area of shapes by counting whole and partial squares.
- Add the areas of different shapes to calculate a total area.
🧠 Key Words
- area
- perimeter
Show Definitions
- area: The amount of space inside a two-dimensional shape, measured in square units such as cm² or m².
- perimeter: The total distance around the outside edge of a two-dimensional shape, found by adding the lengths of all its sides.
Understanding Square Units 📐
I n this topic, you will learn about the square units we use to record the areas of different sizes. These units are important because they help us describe how large or small an area really is. For example, buying tiles to cover a wall with an area of 8 square metres is very different from buying tiles to cover an area of 8 square centimetres.
❓ EXERCISES
1. Estimate the perimeter of these shapes in whole centimetres.
👀 Show answer
🧠 Tip
Remember:
$1$ cm $=$ $10$ mm
$1$ m $=$ $100$ cm
$1$ km $=$ $1000$ m
2.
a. The perimeter of a theme park is $5$ km. How long is the perimeter in metres?
b. The perimeter of this stamp is $6$ cm. How long is the perimeter in millimetres?
c. This is the floor plan of a room. The length of each wall is given in metres.
i. How long is the perimeter of the room in metres?
ii. How long is the perimeter of the room in centimetres?
👀 Show answer
a. $5$ km $= 5000$ m
b. $6$ cm $= 60$ mm
c(i). Add all given side lengths in metres.
c(ii). Multiply the answer in metres by $100$.
3. Which measurement should be used for the area of each of the following things: mm², cm², m² or km²?
a. A pond
b. A puddle
c. A sea
d. A drop of water
👀 Show answer
a. $m^2$
b. $cm^2$
c. $km^2$
d. $mm^2$
❓ EXERCISES
$4$. Count the squares to estimate the area of the island.
👀 Show answer
Each square represents $1\ \text{km}^2$ (because the scale shows $1\ \text{km}$ is the width of one square).
Count the whole squares covered by the island, then add the squares that are more than half covered.
A reasonable estimate from the diagram is about $22\ \text{km}^2$.
$5$. Count the squares to estimate the size of each stain on the baby's bib. Add together your estimates to find an estimate for the total area of the bib that is stained.
👀 Show answer
Each square represents $1\ \text{cm}^2$.
Pink stain: about $6\ \text{cm}^2$
Dark red stain: about $8\ \text{cm}^2$
Orange stain: about $4\ \text{cm}^2$
Green stain: about $2\ \text{cm}^2$
Total stained area $\approx \mathbf{20\ \text{cm}^2}$.
$6$. Lee says that to estimate an area you should only count whole squares.
Zaid says that to estimate an area you should count any square that is partly or wholly covered.
Jo says that to estimate an area you should only count the squares that are more than half covered.
Critique Lee, Zaid and Jo's ideas. Who will get the best estimate? Explain why.
👀 Show answer
Lee: Underestimates because partial squares are ignored.
Zaid: Overestimates because tiny covered parts are counted as full squares.
Jo: Gives the best estimate by balancing under- and overestimation.