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.

Let’s ReviewLet’s Review

A prism is a three-dimensional figure with two parallel and congruent

polygonal bases.

Let’s ReviewLet’s Review

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.

You already know that:

Let’s ReviewCore Lesson

How many different sizes of faces do I see

on this prism?

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

Let’s ReviewCore Lesson triangular base: scalene

# rectangle sizes: 3

Let’s ReviewCore Lesson

Finding surface area:

med.rect.SA = 2( ) + + +tri.

sm.rect.

largerect.

Let’s ReviewCore Lesson triangular base: isosceles

# rectangle sizes: 2

Let’s ReviewCore Lesson

Finding surface area:

SA = 2( ) + + 2( )

tri. smallrect.

largerect.

Let’s ReviewCore Lesson triangular base: equilateral

# rectangle sizes: 1

Let’s ReviewCore Lesson

Finding surface area:

SA = 2( ) + 3( ) tri. rect.

Let’s ReviewCore Lesson

SA = 2( ) + 3( ) tri. rect.

SA = 2( ) + + 2( )

tri. smallrect.

largerect.

med.rect.SA = 2( ) + + +tri.

sm.rect.

largerect.

In this lesson you have learned how to develop a plan for

finding triangular prism surface area by applying your

knowledge of congruent faces.

Let’s ReviewGuided Practice

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

SA = 2( ) + + 2( )

tri. smallrect.

largerect.

Let’s ReviewExtension ActivitiesImagine 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.

Let’s ReviewExtension ActivitiesDarius 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?

Let’s ReviewQuick Quiz

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?