2D shapes and perimeter
🎯 In this topic you will
- Measure the perimeter of shapes by adding side lengths.
- Draw lines, rectangles, and squares, and calculate the perimeter of each shape.
- Explain the difference between regular and irregular shapes.
🧠 Key Words
- centi
- kilo
- perimeter
- regular shape
- irregular shape
- semicircle
Show Definitions
- centi: A metric prefix meaning one hundredth; for example, 1 centimetre is 1/100 of a metre.
- kilo: A metric prefix meaning one thousand; for example, 1 kilometre equals 1000 metres.
- perimeter: The total distance around the outside edge of a shape.
- regular shape: A shape where all sides and all angles are equal.
- irregular shape: A shape where the sides or angles are not all equal.
- semicircle: Half of a circle, formed by cutting a circle along its diameter.
🔷 Regular Polygons
In Stage 2 you learned about regular polygons. A regular polygon is a shape that has all sides and all angles the same size.
🔺 Irregular Polygons
An irregular polygon is a shape that has sides and angles of different sizes.
📏 What Is Perimeter?
The perimeter of a shape is the total length of all of its sides.
❓ EXERCISES
1. Explain what happens to the perimeter when the squares get bigger.
Draw the next two squares in the sequence and write their perimeters.
👀 Show answer
2.
a. Colour the regular shapes.
b. Draw a ring around the irregular shapes.
c. Draw two regular and two irregular shapes of your own. Label them.
👀 Show answer
3. Use ten sticks to make two different shapes that each have a perimeter of $10$ units. Draw what you did.
Try with $12$ sticks. Draw what you did.
👀 Show answer
4. Work out the perimeters of these shapes.
Draw your own irregular shape with a perimeter of $23$ cm. How many lines will you use?
👀 Show answer
b. $14$ cm
c. $18$ m
d. $20$ cm
e. $28$ km
f. Add all given side lengths to find the perimeter.
Final part: any irregular shape totalling $23$ cm is acceptable; number of lines depends on the student’s design.
🧠 Think like a Mathematician
This square has sides measuring $6$ cm.
Show Answers
- a. Perimeter $=4\times6=24$ cm.
- b. Next squares are $5\times5$ and $4\times4$.
Their perimeters are $20$ cm and $16$ cm. - c. Continuing gives squares of sizes $3\times3$, $2\times2$, and $1\times1$.
- d. Perimeters:
$6\times6 \rightarrow 24$
$5\times5 \rightarrow 20$
$4\times4 \rightarrow 16$
$3\times3 \rightarrow 12$
$2\times2 \rightarrow 8$
$1\times1 \rightarrow 4$ - e. Number pattern: $24,\,20,\,16,\,12,\,8,\,4$.
The perimeter decreases by $4$ each time.