Circles
Triangles
Polygons
3D shapes
100
Rosa loves going down to the local park on a Monday afternoon and walk around the pond.
a) Determine the total distance Rosa would travel if she did one lap around the pond?
Use Circumference = π x diameter
b) Determine the area of the walking path?
Use Area = πr2 and π = 3.14
a) Circumference =87.92m
b) Area (path) = 188.4m2
100
What is the name of this triangle?
Bonus 1: What is the sum of the interior angles?
Bonus 2: What is the value of a right angle?
Right triangle
Bonus 1 = 180O
Bonus 2 = 90O
100
Consider the ploygon below:
a) What is its name?
b) how many sides does it have? (express in terms of n = number of sides).
c) Using (n-2) x 180 determine the sum of its interior angles.
d) Determine the value of X?
a) Hexagon
b) n = 6
c) (n-2) x 180 = 720O
d) X = 120O
100
Compare the 3D structures of a pentagonal pyramid and a pentagonal prism.
a) Which one has more faces?
b) Which one has more edges
c) Which one has more vertices?
Bonus: Can you create a rule using the number of side lengths (n) to help you work out the faces, edges and vertices of any pyramid?
a) Faces
Pentagonal pyramid = 6
Pentagonal prism = 7
b) Edges
Pentagonal pyramid = 10
Pentagonal prism = 15
c) Vertices
Pentagonal pyramid = 6
Pentagonal prism = 10
Bonus: rules for pyramids
Faces and vertices = n + 1
Edges = 2n
Check (for pentagonal pyramid, n = 5).
Faces = 5 + 1 = 6
Edges = 2 x 5 = 10
Vertices = 5 + 1 = 6
200
a) State the relationship between radius and diameter of a circle?
b) Determine the diameter of the circle with radius of 10cm
a) Radius = 
x diameter
Diameter = 2 x radius
b) For a circle with radius of 10cm
Diameter = 2 x 10
Diameter = 20cm
200
Consider ΔLMO below.
State the following facts
a) Name of ΔLMO
b) Base
c) Base angles (using
)
d) Vertices
e) Height
a) Isosceles triangle or acute isosceles triangle
b) 
c) 
LOM and LMO
d) Points L, M and O.
e) 
200
Complete the complex analysis of the regular dodecagon shown below:
a) Number of sides (n)?
b) The sum of the interior angles?
c) The value of angle B?
d) The perimeter?
e) The area?
a) n = 12
b) sum of the interior angles = (n-2) x 180
sum of the interior angles =1800O
c) B = 150O
d) Perimeter = 12cm
e) Area = 
x perimeter x apothem
Area = 18cm2
200
True or false, A sphere has 9 faces, 16 edges and 9 vertices.
Bonus: Name the 3D shape the facts would be true for.
False
Bonus: The shape is an octagonal (n=8) pyramid.
300
Circle A has a radius of 5cm. Circle B has a diameter of 9.98cm. Which circle is larger?
Compare diameters:
Diameter of circle A = 10cm
Diameter of circle B = 9.98cm
10cm > 9.98cm
Circle A is larger
300
Andy is feeling hungry, so he grabs some Doritos on his way home from school. They are his favorite snack because of the chips fun triangular shape.
One chip has a base of 4cm, a height of 5cm and weighs approximately 2g. Considering this information answer the following questions:
a) What type of triangle is the Doritos chip if you classify it based on side length?
b) Determine the total surface of 1 chip (front and back)?
Bonus 1: If Andy gets a 60g bag, what would be the total surface area of all the chips in it?
Bonus 2: If the 60g bag contains 6g of pressurized air to help preserve the chips, how many chips would actually be the bag? what percentage of the total weight do the chips contribute?
a) Equilateral triangle
b) Area of one side = 10cm2 x 2
Total surface area = 20cm2
Bonus 1: 600cm2
Bonus 2: 27 chips = 90%
300
Determine which shape is the largest?
a) A circle with diameter of 6cm,
Area = πr2 and π = 3.14.
b) A triangle with base of 6cm and a height of 10cm
Area = 
x base x height.
c) A pentagon with a side length of 4cm and an apothem of 2.9cm.
Area =
x perimeter x apothem
a) Area (circle) = 28.26cm2
b) Area (triangle) = 30cm2
c) Area (pentagon) = 29cm2
triangle > pentagon > circle
The triangle is the largest
300
Draw the net diagram of a hexagonal pyramid.
a) Record how may triangles and how many hexagons you can see.
b) Determine the number of faces, edges and vertices it has.
a) 6 triangles and 1 hexagon
b) Faces = 7
Edges = 12
Vertices = 7
400
A circle has a diameter of 20mm.
a) Using Circumference = π x diameter and π = 3.14 determine the circumference of this circle?
b) Using Area = πr2 and π = 3.14 determine the area of this circle?
a) Circumference = 62.8mm
b) Area = 314mm2
400
Determine the values of each interior angle in the diagram below.
a) TWX and XTW
b) UTW and TWU
c) WUV
a)TWX = XTW = 45O
b) UTW = 45O,TWU= 80O
c) WUV = 61O
400
Consider the irregular pentagon (n = 5) below.
Determine the values of the two unknown interior angles using (n-2) x 180 shown.
X = 70O
2X = 140O
400
What are the names of the 3D shapes shown below?
a)
b)
c)
d)
a) Cone
b) Cube
c) square pyramid
d) Cylinder
500
What do each of the letters represent in the diagram?
A?
B?
C?
A = Centre
B = Radius
C = Diameter
500
Determine the perimeter and area of a right triangle with base of 3m and height of 4m?
Area = x base x height.
Perimeter = 12m
Area = 6m2
500
You are a tiler who has been asked to work on a new house being built. The kitchen looks like the diagram below.
There is a bench that sits in the middle of the kitchen with a length of 4 meters and a width of 1 meter. You must tile around the bench.
You have the choice of using two tiles.
- Option 1: Rectangular tile with a length of 2 meters and width of 1m.
- Option 2: Pentagonal tile with side lengths of 0.4 meters and an apothem of 0.5 meters.
From the option you choose work out how many tiles you will need to cover the entire kitchen floor.
Bonus: Consider the costs for the two tiles.
- Rectangular tiles cost 100 baht per tile.
- Pentagonal tiles cost 22 baht and 40 satang (22.4 baht) per tile.
If the homeowner has a budget 2100 baht, which tile must you use?
Option 1: 23 rectangular tiles
Option 2: 92 pentagonal tiles
Bonus: You must use the pentagonal tile.
500
How many faces, edges and vertices would an pentecontagonal pyramid (n = 50) pyramid have?
Faces = 51
Edges = 100
Vertices = 51