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 ① ② ⑥ ③ ④ ⑤ ① ② ③ ④ ⑤ ⑥ = 32cm 5 cm 6 cm 5 cm 2 cm Perimeter = 5cm + 3cm + 6cm + 2cm + 11cm + 5cm = 32cm

Example Perimeter = 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 60 m 5 m 10 m 20 m Block B 25 m 40 m 40 m 10 m 20 m Block A 30 m 10 m 50 m 60 m Who walks the greatest distance? Explain your answer.

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 110 m 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 Radius 2. 4. Centre 1. Arc 5. Sector 3. Diameter 6. Segment 7. Chord 8. Circumference 9. Tangent

Circle Geometry The perimeter of a circle is called the circumference. Activity: Draw a circle on a sheet of paper Measure the circles radius and diameter With a piece of string (or something similar) measure the circumference of the circle Repeat for 3 more circles of difference sizes Record your findings on the table shown on the next slide

Circle Geometry Questions: Radius Diameter Circumference Questions: Do you see any relationship between the diameter and the circumference? Do you see any relationship between the radius and the circumference? Can you write the circumference in terms of the diameter? Can you write the circumference in terms of the radius?

Circumference = C C = 2πr or C = πd (d=2r) r 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 it is 𝜽 𝟑𝟔𝟎 of the circle = 𝜽 𝟑𝟔𝟎 ×𝟐𝝅𝒓 Therefore the arc length is

Arc Length and Perimeter Example: Find the perimeter of the sector Angle of sector = 360° - 120 ° = 240 ° Arc Length = 𝜃 360 ×2𝜋𝑟 = 240 360 ×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