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How can you decide how much material you’ll need to construct a tent like this one?. In this lesson you will learn how to develop a plan for finding triangular prism surface area by applying your knowledge of congruent faces.

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Presentation Transcript
slide2
In this lesson you will learn how to develop a plan for finding triangular prism surface area by applying your knowledge of congruent faces.
slide4

You already know that:

  • Triangular prisms with equilateral triangle bases have rectangular faces that are all exactly congruent.
  • Triangular prisms with isosceles triangle bases have rectangular faces that comes in 2 different sizes.

Triangular prisms with scalene triangle bases have rectangular faces that come in 3 different sizes.

slide5

When developing a plan to find surface area, you must ask yourself:

How many different sizes of faces do I see on this prism?

slide6

triangular base: scalene

# rectangle sizes: 3

slide7

Finding surface area:

sm.

rect.

med.

rect.

large

rect.

SA=2( ) + + +

tri.

slide8

triangular base: isosceles

# rectangle sizes: 2

slide9

Finding surface area:

small

rect.

large

rect.

SA=2( ) + + 2( )

tri.

slide10

triangular base: equilateral

# rectangle sizes: 1

slide11

Finding surface area:

SA=2( ) + 3( )

rect.

tri.

slide12

small

rect.

large

rect.

SA=2( ) + + 2( )

tri.

sm.

rect.

med.

rect.

SA=2( ) + 3( )

rect.

large

rect.

tri.

SA=2( ) + + +

tri.

slide13

In this lesson you have learned how to develop a plan for finding triangular prism surface area by applying your knowledge of congruent faces.

slide14

Write down your plan for finding the surface area of this triangular prism.

small

rect.

SA=2( ) + + 2( )

large

rect.

tri.

slide15

Imagine that the three shapes (A, B, and C, below) represent the bases of three different triangular prisms.

  • Describe how your plan for finding the surface area of a prism with base A would differ from your plan for finding the surface area of a prism with base B or base C.

A.

B.

C.

slide16

Darius says, “To find the surface area of a triangular prism, first you find the area of the triangular base. Then, you find the area of one of the three rectangular faces, and add that to the area of the triangular base. Then you’re done!”

  • Explain to Darius why his explanation is not entirely correct. What did he leave out?
slide17

What plan would you use to find the surface area of a triangular prism with a scalene triangle base?

What plan would you use to find the surface area of a triangular prism with an equilateral triangle base?