Understanding Triangular Prism Surface Area
A triangular prism is a three-dimensional solid shape with two identical faces that are triangles and three rectangular faces. The surface area of a triangular prism is the total area of all its faces. In this worksheet, we will explore how to calculate the surface area of a triangular prism.
Formula for Triangular Prism Surface Area
The formula for the surface area of a triangular prism is:
SA = 2 × (Base Area) + (Perimeter of Base × Height)
Where:
- SA is the surface area of the triangular prism
- Base Area is the area of one of the triangular faces
- Perimeter of Base is the perimeter of one of the triangular faces
- Height is the height of the prism
Calculating Base Area
To calculate the base area of a triangular prism, you need to know the length of the base and the height of the triangle. The formula for the area of a triangle is:
A = (1⁄2) × Base × Height
Where:
- A is the area of the triangle
- Base is the length of the base of the triangle
- Height is the height of the triangle
Calculating Perimeter of Base
To calculate the perimeter of the base of a triangular prism, you need to know the length of all three sides of the triangle. The formula for the perimeter of a triangle is:
P = Side1 + Side2 + Side3
Where:
- P is the perimeter of the triangle
- Side1, Side2, and Side3 are the lengths of the three sides of the triangle
Example Problems
Now, let’s practice calculating the surface area of a triangular prism with some example problems.
Problem 1
Find the surface area of a triangular prism with a base area of 12 square units, a perimeter of 18 units, and a height of 5 units.
Solution:
SA = 2 × (Base Area) + (Perimeter of Base × Height) = 2 × 12 + (18 × 5) = 24 + 90 = 114 square units
Problem 2
Find the surface area of a triangular prism with a base length of 8 units, a base height of 6 units, and a height of 4 units.
Solution:
First, calculate the base area: A = (1⁄2) × Base × Height = (1⁄2) × 8 × 6 = 24 square units
Next, calculate the perimeter of the base: P = Side1 + Side2 + Side3 = 8 + 8 + 6 = 22 units
Now, calculate the surface area: SA = 2 × (Base Area) + (Perimeter of Base × Height) = 2 × 24 + (22 × 4) = 48 + 88 = 136 square units
Practice Problems
Here are some practice problems for you to try:
- Find the surface area of a triangular prism with a base area of 15 square units, a perimeter of 20 units, and a height of 6 units.
- Find the surface area of a triangular prism with a base length of 10 units, a base height of 8 units, and a height of 5 units.
- Find the surface area of a triangular prism with a base area of 20 square units, a perimeter of 25 units, and a height of 7 units.
📝 Note: Remember to use the formulas and steps outlined above to solve these problems.
What is the formula for the surface area of a triangular prism?
+SA = 2 × (Base Area) + (Perimeter of Base × Height)
How do I calculate the base area of a triangular prism?
+A = (1/2) × Base × Height
What is the perimeter of a triangle?
+P = Side1 + Side2 + Side3
In conclusion, calculating the surface area of a triangular prism requires knowledge of the base area, perimeter of the base, and height of the prism. By using the formulas and steps outlined in this worksheet, you can easily calculate the surface area of a triangular prism.
