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How can you decide how much material you’ll need to construct a tent like this one?

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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How can you decide how much material you’ll need to construct a tent like this one?

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  1. How can you decide how much material you’ll need to construct a tent like this one?

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

  3. A prism is a three-dimensional figure with two parallel and congruent polygonal bases.

  4. 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.

  5. When developing a plan to find surface area, you must ask yourself: How many different sizes of faces do I see on this prism?

  6. triangular base: scalene # rectangle sizes: 3

  7. Finding surface area: sm. rect. med. rect. large rect. SA=2( ) + + + tri.

  8. triangular base: isosceles # rectangle sizes: 2

  9. Finding surface area: small rect. large rect. SA=2( ) + + 2( ) tri.

  10. triangular base: equilateral # rectangle sizes: 1

  11. Finding surface area: SA=2( ) + 3( ) rect. tri.

  12. small rect. large rect. SA=2( ) + + 2( ) tri. sm. rect. med. rect. SA=2( ) + 3( ) rect. large rect. tri. SA=2( ) + + + tri.

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

  14. Write down your plan for finding the surface area of this triangular prism. small rect. SA=2( ) + + 2( ) large rect. tri.

  15. 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.

  16. 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?

  17. 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?

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