6th Grade Math Textbook, Progress

Surface Area of Pyramids and

Triangular Prisms

13-15

To find the surface area of a square pyramid:

• Open the pyramid to form its net.


• Find the area of each of its 5 faces.


• Add the areas to get the surface area.

Area of base 
6 cm6 cm 
 36 cm^2

Area of faces
4(^12 ) (6 cm5 cm) 
 60 cm^2

Surface Area (S)
 96 cm^2

When the 4 triangular faces of a square pyramid are congruent,

use a shortcut to find the surface area. Find the area of one triangular

face, multiply by 4, and add that to the area of the square base.

S
4 (Atriangle) Asquare


 4 ^12 (6 cm5 cm)(6 cm)^2


 60 cm^2 36 cm^2


 96 cm^2

To find the surface area of a triangular prism:

• Open the prism to form its net.


• Find the area of each of its 5 faces.


• Add the areas to get the total area.

Area of bottom face 
18 mm21 mm 
 378 mm^2

Area of rectangular front and back faces
2 (21 mm15 mm) 
 630 mm^2

Area of triangular bases 
 2 ^12 (18 mm12 mm)
216 mm^2

Surface Area (S)
 1224 mm^2

In this square pyramid, the

4 triangular faces are congruent.

In this triangular prism, the triangular

bases are congruent and the front and

back rectangular faces are congruent.

6 cm

6 cm

h 
 5 cm

front

side base side

back

front

side bottom side

back

18 mm 21 mm

15 mm

h 
 12 mm

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