Surface Area of Prisms and Cylinders

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.

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

Prisms are classified by the shapes of their bases

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

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):

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

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

Example

Example

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

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

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

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

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

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