Understanding Surface Area of Prisms
In geometry, a prism is a three-dimensional solid object with two identical faces that are parallel and oriented in the same direction. The surface area of a prism is the total area of its faces, including the two identical faces and the lateral faces. In this worksheet, we will explore the concept of surface area of prisms and learn how to calculate it.
Types of Prisms
There are several types of prisms, including:
- Rectangular prism: A prism with rectangular faces.
- Triangular prism: A prism with triangular faces.
- Pentagonal prism: A prism with pentagonal faces.
- Hexagonal prism: A prism with hexagonal faces.
Surface Area of a Rectangular Prism
The surface area of a rectangular prism can be calculated using the formula:
SA = 2lw + 2lh + 2wh
Where:
- l is the length of the prism.
- w is the width of the prism.
- h is the height of the prism.
For example, find the surface area of a rectangular prism with a length of 6 cm, a width of 4 cm, and a height of 3 cm.
SA = 2(6)(4) + 2(6)(3) + 2(4)(3) SA = 48 + 36 + 24 SA = 108
Surface Area of a Triangular Prism
The surface area of a triangular prism can be calculated using the formula:
SA = 2(l × w) + (b × h) + (c × h)
Where:
- l is the length of the prism.
- w is the width of the prism.
- b is the base of the triangular face.
- c is the height of the triangular face.
- h is the height of the prism.
For example, find the surface area of a triangular prism with a length of 5 cm, a width of 3 cm, a base of 4 cm, a height of 6 cm, and a height of the prism of 4 cm.
SA = 2(5)(3) + (4)(4) + (6)(4) SA = 30 + 16 + 24 SA = 70
Surface Area of a Pentagonal Prism
The surface area of a pentagonal prism can be calculated using the formula:
SA = 2(l × w) + (b × h) + (c × h) + (d × h) + (e × h)
Where:
- l is the length of the prism.
- w is the width of the prism.
- b, c, d, and e are the bases of the pentagonal faces.
- h is the height of the prism.
For example, find the surface area of a pentagonal prism with a length of 6 cm, a width of 4 cm, bases of 5 cm, 6 cm, 7 cm, and 8 cm, and a height of 5 cm.
SA = 2(6)(4) + (5)(5) + (6)(5) + (7)(5) + (8)(5) SA = 48 + 25 + 30 + 35 + 40 SA = 178
Surface Area of a Hexagonal Prism
The surface area of a hexagonal prism can be calculated using the formula:
SA = 2(l × w) + (b × h) + (c × h) + (d × h) + (e × h) + (f × h)
Where:
- l is the length of the prism.
- w is the width of the prism.
- b, c, d, e, and f are the bases of the hexagonal faces.
- h is the height of the prism.
For example, find the surface area of a hexagonal prism with a length of 7 cm, a width of 5 cm, bases of 6 cm, 7 cm, 8 cm, 9 cm, and 10 cm, and a height of 6 cm.
SA = 2(7)(5) + (6)(6) + (7)(6) + (8)(6) + (9)(6) + (10)(6) SA = 70 + 36 + 42 + 48 + 54 + 60 SA = 310
📝 Note: The formulas for the surface area of prisms can be used to find the total area of the faces of the prism.
Practice Problems
- Find the surface area of a rectangular prism with a length of 8 cm, a width of 5 cm, and a height of 4 cm.
- Find the surface area of a triangular prism with a length of 6 cm, a width of 4 cm, a base of 5 cm, a height of 7 cm, and a height of the prism of 5 cm.
- Find the surface area of a pentagonal prism with a length of 7 cm, a width of 5 cm, bases of 6 cm, 7 cm, 8 cm, and 9 cm, and a height of 6 cm.
Table of Formulas
| Type of Prism | Formula for Surface Area |
|---|---|
| Rectangular Prism | SA = 2lw + 2lh + 2wh |
| Triangular Prism | SA = 2(l × w) + (b × h) + (c × h) |
| Pentagonal Prism | SA = 2(l × w) + (b × h) + (c × h) + (d × h) + (e × h) |
| Hexagonal Prism | SA = 2(l × w) + (b × h) + (c × h) + (d × h) + (e × h) + (f × h) |
To summarize, the surface area of a prism can be calculated using different formulas depending on the type of prism. The formulas for the surface area of rectangular, triangular, pentagonal, and hexagonal prisms are provided above. By using these formulas, you can find the total area of the faces of the prism.
What is the formula for the surface area of a rectangular prism?
+The formula for the surface area of a rectangular prism is SA = 2lw + 2lh + 2wh.
What is the formula for the surface area of a triangular prism?
+The formula for the surface area of a triangular prism is SA = 2(l × w) + (b × h) + (c × h).
What is the formula for the surface area of a pentagonal prism?
+The formula for the surface area of a pentagonal prism is SA = 2(l × w) + (b × h) + (c × h) + (d × h) + (e × h).
