MEASUREMENT
Perimeter
Perimeter
• Is the path that surrounds a two-dimensional shape.
• The word perimeter comes from the Greek peri (around) and meter (measure).
• It can be thought of as the length of the outside of a shape.
• The perimeter is measured in the same units as those for length (i.e. cm, m etc)
• To find the length of a shape, simply add together the individual lengths.
• Sometimes you may have to calculate the length of missing sides from the
information provided, using symmetry or other properties of shapes.
Example
5 cm
①
5 cm
②
6 cm
⑥
③
④
⑤
①
②
③
④
⑤
⑥
Perimeter = 5cm + 3cm + 6cm + 2cm + 11cm + 5cm
= 32cm
2 cm
Example
4.5 m
Perimeter
1.7 m
= 4.5m + 1.7m + 4.5m + 1.7m
= 12.4m
The line means that the top horizontal line is the same length as the bottom
horizontal line
The
lines means that the right vertical line is the same length as the left
vertical line
Example
Blake and Renee compare the distance they walk around the school grounds.
Blake walks around Block A, and Renee walks around Block B.
20 m
10 m
60 m
5m
20 m
25 m
10 m
30 m
Block A
20 m
40 m
Block B
10 m
50 m
Who walks the greatest distance? Explain your answer.
60 m
40 m
Example
Kelvin plans to plan a shelter belt
Paddock
110 m
around this paddock. He will plant
trees 2 metres apart, starting a corner.
How many trees will he need to plant?
450 m
ANSWER = 560 trees
Circle Geometry
In your groups, write down as many words as you can
think of that relate to a circle and its geometric
properties.
Circle Geometry
Circle Geometry
Circle Geometry
Parts of a Circle
1.
Arc
2. Radius
4. Centre
3. Diameter
6. Segment
7. Chord
5. Sector
8. Circumference 9. Tangent
Circle Geometry
The perimeter of a circle is called the circumference.
Activity:
1. Draw a circle on a sheet of paper
2. Measure the circles radius and diameter
3. With a piece of string (or something similar) measure the circumference of
the circle
4. Repeat for 3 more circles of difference sizes
5. Record your findings on the table shown on the next slide
Circle Geometry
Circle #
Radius
Diameter
Circumference
Questions:
1. Do you see any relationship between the diameter and the circumference?
2. Do you see any relationship between the radius and the circumference?
3. Can you write the circumference in terms of the diameter?
4. Can you write the circumference in terms of the radius?
Circumference =
C
C = 2πr
or
C = πd
(d=2r)
Example
Calculate the circumference of a circle
which has a radius of 32 cm.
C = 2πr
= 2 × π × 32
= 201.1 cm (4 sf)
Circumference change of formula
To calculate the radius, when given the circumference, we need to
rearrange the formula to make r the subject.
C = 2πr
r= C
2π
Example
Calculate the radius of a circle that has a circumference of
11.5 m
r = 11.5
2π
r = 1.83 m (2dp)
Arc Length
If a sector has an angle at the centre equal to 𝞱, then what would the
arc length be?
arc length
𝞱 is what proportion of the total circle?
𝞱
Therefore the arc length is
it is
𝜽
𝟑𝟔𝟎
of the circle
𝜽
=
× 𝟐𝝅𝒓
𝟑𝟔𝟎
Arc Length and Perimeter
Example: Find the perimeter of the sector
Angle of sector = 360° - 120 ° = 240 °
Arc Length =
𝜃
360
240
=
360
× 2𝜋𝑟
×2 × 𝜋 ×6
= 25.1m (1dp)
Perimeter = 2 x 6m + 25.1m
= 37.1m
Problem
Find the perimeter of this shape that is formed using 3
semicircles (2dp)
ANSWER = 38.96 cm (2dp)
Homework
2d shapes: Exercise D: Pages 164-165
Circles :
Exercise E: Pages 167-169