Unit 4: Surface Area of Prisms and Pyramids
Vocabulary:
Net: a 2-dimensional flat pattern that can be folded into a 3-dimensional figure.
Surface Area: the total area of all the faces of a solid figure.
Congruent: equal
4-1: Surface Area of Rectangular Prisms
Find the surface area of the rectangular prism.
**Formula: SA = 2lw + 2wh + 2lh (l = length w = width h = height)
SA = (2 · 3 · 2) + (2 · 2 · 6) + (2 · 3 · 6)
SA = 12 + 24 + 36
SA = 72 cm²
4-2: Prisms are Named by the Shape of their Bases.
Base Shape: Triangle
Net:
Prism Name: Triangular Prism
Base Shape: Hexagon
Net:
Prism Name: Hexagonal Prism
4-3: Surface Area of Prisms
Example 1:
Step 1: Look for the basic shapes that make up the figure.

Basic Shapes: 2 congruent triangles, 3 different rectangles
Step 2: Find the area of each basic shape.

Area of 1 triangle: A =
A=
A=
𝑏ℎ
2
3 ·4
2
12
2
(There are 2 triangles) A = 6 ft² (multiply by 2)
A = 12 ft²
=h
l=
=w

Area of Rectangle #1: A = bh
A=4·7
A = 28 ft²
Area of Rectangle #2: A = bh
A=7·5
A = 35 ft²
Area of Rectangle #3: A = bh
A=3·7
A = 21 ft²
Step 3: Add the areas of the shapes together.

12 + 28 + 35 + 21 = 96
SA = 96 ft²
Example 2:
Step 1: Look for the basic shapes that make up the figure.

Basic Shapes: 2 congruent hexagons, 6 congruent rectangles
Step 2: Find the area of each basic shape.

Area of 1 hexagon: A =
A=
𝑏ℎ
n (multiply by # of sides denoted by n)
2
4 ·3
A=
(6)
2
10 in
12
2
(6)
A = 6(6) in²
(There are 2 hexagons) A = 36 in² (multiply by 2)
A = 72 in²

Area of 1 rectangle: A = bh
A = 4 · 10
(There are 6 rectangles) A = 40 in² (multiply by 6)
A = 240 in²
3 in
Step 3: Add the areas of the shapes together.

72 + 240 = 312
SA = 312 in²
4-4: Pyramids are Named by the Shape of their Bases
Base Shape: Square
Pyramid Name: Square Pyramid
Net:
Base Shape: Pentagon
Prism Name: Pentagonal Pyramid
Net:
4 in
4-5: Surface area of Pyramids
Example 1:
Step 1: Look for the basic shapes that make up the figure.
 Basic Shapes: 1 square, 4 congruent triangles
Step 2: Find the area of each basic shape.
 Area of the square: A = bh
A=5·5
A = 25 ft²

Area of 1 triangle: A =
A=
A=
6 ft
𝑏ℎ
2
5 ft
5 ft
5 ·6
2
30
2
(There are 4 triangles) A = 15 ft² (multiply by 4)
A = 60 ft²
Step 3: Add all of the areas together.
 25 + 60 = 85
SA = 85 ft²
Example 2:
Step 1: Look for the basic shapes that make up the figure.
 Basic Shapes: 1 pentagon, 5 congruent triangles
Step 2: Find the area of each basic shape.

Area of the pentagon: A =
𝑏ℎ
A=
A=
n (n is the number of sides)
2
8 ·6
2
48
2
(5)
(5)
A = 24(5)
A = 24(5) (multiply by 5 sides)
A = 120 in²

Area of 1 triangle: A =
A=
A=
12 in
𝑏ℎ
2
8 ·12
2
96
2
(There are 5 triangles) A = 48 in² (multiply by 5)
A = 240 in²
Step 3: Add all of the areas together.
 120 + 240 = 360
SA = 360 in²
6 in
8 in