Download Unit 1 Lesson 4.notebook

Unit 1 Lesson 4.notebook
September 22, 2016
Math 1201: Unit 1 Lesson 4
Surface Area of Right Pyramids
Surface Area: the sum of the areas of all faces of a 3 dimensional figure.
A right pyramid is a 3­D figure with a polygon base and triangular faces. The shape of the base determines the name of the pyramid. We will examine right pyramid with a triangular base, square base, and a rectangular base. When the base of a right pyramid is a regular polygon, the triangular faces are congruent (regular pyramid). The triangular faces meet at a point called the apex. The height of the pyramid is the perpendicular distance from the apex to the centre of the base.
height
height
Notice that the slant height is different from the height of the pyramid.
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Unit 1 Lesson 4.notebook
September 22, 2016
We will examine right pyramids that have bases in the following shapes:
• triangular
• square
• rectangular
Regular tetrahedron (triangular base)
ie.
Regular tetrahedron: has 4 congruent equilateral triangular faces.
Right Square Pyramid (square base)
ie.
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Unit 1 Lesson 4.notebook
September 22, 2016
Right Rectangular Pyramid (rectangle base)
ie.
Example 1 Determine the surface area of the given regular tetrahedron.
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Unit 1 Lesson 4.notebook
September 22, 2016
Example 2 Determine the surface area of the right square prism, to the nearest tenth.
Example 3 Determine the surface area of the right rectangular prism, to the nearest square metre.
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Unit 1 Lesson 4.notebook
September 22, 2016
Working Backwards: Surface Area Given
Example: A right square pyramid has a surface area of 72.4 m2 and the square base has a side length of 4.6 m. What is the slant height of the pyramid?
Total Surface Area vs. Lateral Area
Total Surface Area: the sum of ALL the faces of a figure. For the prism shown below, the total surface area would include the sum of the areas of the 4 triangular sides and the base.
Lateral Area: the sum of the sides of a figure EXCLUDING the base. For the prism shown below, the lateral area would include the sum of the areas of the 4 triangular sides only (the base would NOT be included).
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Unit 1 Lesson 4.notebook
September 22, 2016
Example: Consider the prism shown below:
14 cm
9 cm
(A) Determine the total surface area.
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Unit 1 Lesson 4.notebook
September 22, 2016
(B) Determine the lateral area.
QUESTIONS: p. 34­35 #4, 5, 8(a), 13(a), 16(b) 7