1. Surface Area of Prisms and Cylinders

2. Area
The area of a shape is a measure of how much surface the shape takes up.
Discuss how we can compare the area of the rugs by counting the squares that make up each pattern.
Conclude that Rug B covers the largest surface.

3. Prisms & Cylinders
Polyhedron – a solid bounded by polygons (a 3D figure)
Prism – a polyhedron with two congruent parallel faces called bases
Cylinder – a solid with congruent circular bases that lie in parallel planes
radius
base
base
height
Lateral face (4)
base
base

4. Prisms are classified by the shapes of their bases

5. Rectangles
The perimeter of a rectangle with length l and width w can be written as: l w
Perimeter = 2l + 2w or
Perimeter = 2(l + w)
The area of a rectangle is given as:
Area = lw

6. Triangles
The area of a triangle is found by multiplying the base (b) times the height (h) and dividing by 2 (or multiplying by ½):

7. Surface Area verses Lateral Area of a Prism
The lateral area of a polyhedron or prism is the sum of the area of its lateral faces (without getting the area of the bases).
LA = Ph P = Perimeter of the base
h = height of 3-D shape
base
Lateral face (4)
base

8. Surface Area verses Lateral Area of a Prism
The surface area of a polyhedron or prism is the sum of area of its faces (including the area of the bases).
SA = Ph + 2B P = Perimeter of the base
h = height of 3-D shape
B = Area of the base
base
Lateral face (4)
base

9. Example

10. Example

11. The circumference of a circle
For any circle,
The Circumference is found through the formula:
C = πd
Inversely, if you have the circumference, you can find the diameter through the formula:
Pupils should be asked to learn these formulae.
diameter =
circumference π

12. Formula for the area of a circle
We can find the area of a circle using the formula
Area of a circle = π × r × r
radius or
Area of a circle = πr2

13. Surface Area verses Lateral Area of a Cylinder
The lateral area of a cylinder is the area of its curved surface.
LA = r = radius of the base
h = height of 3-D shape
radius
base
height
base

14. Surface Area verses Lateral Area of a Cylinder
The surface area of a cylinder is equal to the sum of the lateral area and the areas of the two bases.
SA =
radius
base
height
base

15. Scaling If we scale the dimensions of a prism or any other 3D
figure, we are multiplying each dimension (length, width, height, etc) by the scale factor.
For example, if we have the following figure and scale it by 2,
It’s new dimensions are 4 cm by 10 cm, by 20 cm

16. Homework Page 16-17, #6, 7 Page 18, #11A-C Page 22, #24 Page 59, #8-10