MEASUREMENTPerimeter

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

6 cm

5 cm

2 cm

5 cm

Perimeter = 5cm + 3cm + 6cm + 2cm + 11cm + 5cm

= 32cm

①②

③⑥

⑤④

① ② ③ ④ ⑤ ⑥

Example

4.5 m

1.7 m

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

Perimeter = 4.5m + 1.7m + 4.5m + 1.7m

= 12.4m

ExampleBlake and Renee compare the distance they walk around the school grounds. Blake walks around Block A, and Renee walks around Block B.

Block A

Who walks the greatest distance? Explain your answer.

25 m

20 m

10 m 20 m

30 m 10 m

50 m

5 m

20 m

10 m

60 m

60 m

40 m 40 mBlock B

Example

Kelvin plans to plan a shelter belt

around this paddock. He will plant

trees 2 metres apart, starting a corner.

How many trees will he need to

plant?

Paddock

450 m

110 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 CircleArc

Radius

Diameter

Centre

Segment Chord

Sector

Circumference Tangent7.

3.

2. 4.

5.

6.

1.

8. 9.

Circle GeometryThe 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 =

r

C = 2πr or C = πd (d=2r)C

ExampleCalculate 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 formulaTo calculate the radius, when given the circumference, we need to rearrange the formula to make r the subject.

C = 2πr r = C 2π

ExampleCalculate the radius of a circle that has a circumference of 11.5 m

r = 11.5 2π

r = 1.83 m (2dp)

Arc LengthIf a sector has an angle at the centre equal to 𝞱, then what would the arc length be?

𝞱arc length

𝞱 is what proportion of the total circle?it is of the circleTherefore the arc length is ¿ 𝜽

𝟑𝟔𝟎×𝟐𝝅𝒓

Arc Length and Perimeter

Example: Find the perimeter of the sector

Angle of sector = 360° - 120 ° = 240 °

Arc Length =

=

= 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 164-165Circles : Exercise E: Pages 167-169