Lesson 2 of 3

WRAPPING UP GEOMETRY

Learning Objective: Today we will explore how to represent triangular prisms using nets and fi nd the surface area of a triangular prism.

WRAPPING UP GEOMETRY – SURFACE AREA

top

bottom

top

bottom

backback side front side

SURFACE AREA…WHEN YOU THINK ABOUT THE WORDS SURFACE AND AREA AND PUT THEM

TOGETHER…

= +

+

++

QUICK WRITESilently, in your own words, describe what the

diagram means in terms of a definition of surface area.

= +

+

++

Let’s take a look at what finding the surface area means in a triangular prism…

6 in

ches

7 inch

es

11 inches

14 inches

14

inches

The bases of the triangular prism are the…triangles (we name prisms after their base shapes.) We know which faces are the bases because they are congruent to each other and parallel to each other.

The lateral faces of the triangular prism are…rectangles (prism faces are ALWAYS rectangles.)

When you create the net, label each face as a base

or lateral face, then with the correct measures.

14 inches

14 inches

11 inches 7 inches

7 inches

11 inches

6 in

ches

lateral face

lateral face

lateral facebase base

BREAK THE NET DOWN INTO THE SUM OF ITS PARTS…

11 inches

11 inches

+6 inches

6 inches

+7 inches

6 inches

7 inches

14 inches

7 inches

14 inches

+

+B

ASES

LATER

AL

FAC

ES

BREAK THE PRISM DOWN INTO THE SUM OF ITS FACES BY LOOKING AT THE NET’S

AREA…START WITH THE BASE AREA

6 inches

11 inches

The formula for the area of a triangle is:𝑨=

𝟏𝟐

(𝟔 𝒊𝒏𝒄𝒉𝒆𝒔 ) (𝟏𝟏𝒊𝒏𝒄𝒉𝒆𝒔 )

𝑨=𝟑𝟑𝒊𝒏𝟐

There are two triangles in the net, so 2A = 66 in2

The area for a rectangle is: 𝑨=𝒃𝒉

7 inches

14 inches

𝐴= (7 h𝑖𝑛𝑐 𝑒𝑠 )(14 h𝑖𝑛𝑐 𝑒𝑠)𝐴=98 𝑖𝑛2There are two rectangles this size, so

7 inches6

inches

𝐴= (7 h𝑖𝑛𝑐 𝑒𝑠 )(6 h𝑖𝑛𝑐 𝑒𝑠)

𝑨=𝟒𝟐 𝒊𝒏𝟐

The faces on the side (lateral faces) sum to 238 in2

Then find the lateral face areas…

FIND THE SUM OF THE BASE AREAS AND THE LATERAL FACE AREAS…

+42 in2

98 in2

98 in2

LATER

AL

FAC

ES

33 in2

+

BA

SES

33 in2

66 in2 +238 in2Surface Area =304 in2

+

+

NOW YOU TRY IT…

• Sketch a 2-D net of this 3-D triangular prism and label the measures of each face correctly.

• Identify the bases and lateral faces.

20 cm 16

cm

18 cm

11 cm

15 cm

base

bottom

base

right faceleft face

11 cm

20 cm

18 cm

15 cm

15 cm

15 cm

18 cm

18 cm

11 cm

11 cm

From Prism to Net…

135 cm2

135 cm2

198 cm211 cm

20 cm

18 cm

15 cm

15 cm

15 cm

18 cm

18 cm

11 cm

11 cm165 cm2

198 cm2

FIND EACH FACE’S AREA, THEN SUM THEM UP…

135 cm2

135 cm2

198 cm2

198 cm2

+165 cm2

831 cm2

• Break the prism into the sum of the area of its faces• Sketch a net of the prism• Compute the area of each prism

face• Sum up the areas of each face

Wrap UpSurface Area of Triangular

Prisms