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
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