Triangular Prism Calculator: This tool is essential for anyone looking to quickly and accurately determine the volume and surface area of a triangular prism. A triangular prism is a type of prism with two triangular bases and three rectangular faces connecting them. The website GeeksforGeeks has developed a simple and fast triangular prism calculator that always gives you the right answer. This calculator is versatile and can be used by a student, teacher, or professional, understanding how to use these calculations can help you with projects, homework, or real-world applications.
How to Use Triangular Prism Calculator
Let's look into the manual calculation process. Here's a simple three-step method along with the formulas for finding the properties of a triangular prism:
1. Surface Area:
- Calculate the area of each triangular base.
- Multiply the perimeter of the base triangle by the height of the prism and divide by two.
- Add the areas of the two triangular bases and the three rectangular faces.
2. Volume:
- Calculate the area of the triangular base.
- Multiply the area of the base by the height of the prism.
3. Lateral Surface Area:
- Calculate the perimeter of the base triangle.
- Multiply the perimeter by the height of the prism.
What is Triangular Prism Calculator?
A triangular prism calculator serves as a helpful guide for individuals needing to perform manual calculations without depending on tools or software. It empowers users to understand the calculation process and enables them to specify various properties of triangular prisms independently. By following the steps outlined in this article, you'll gain confidence in calculating triangular prism properties accurately.
Triangular Prism Calculator Formula
A triangular prism calculator uses a formula to help you find different aspects of the prism, like its volume and surface area.
To calculate the volume of a triangular prism, you multiply the area of the triangle base by the length of the prism. The formula is:
Volume = Base Area × Length
The base area of the triangle is found by using the formula:
Base Area = 1/2 × base × height
To find the surface area of the triangular prism, you need to calculate the area of all its sides and then add them together. The formula includes the areas of the three rectangular sides and the two triangular bases.
Triangular Prism Calculator Table
Here's a convenient table showcasing properties of triangular prisms with different dimensions:
Height
| Base Side 1
| Base Side 2
| Base Side 3
| Surface Area
| Volume
| Lateral Surface Area
|
|---|
5
| 4
| 7
| 8
| 202
| 100
| 85
|
8
| 6
| 10
| 12
| 396
| 480
| 140
|
10
| 8
| 12
| 15
| 620
| 720
| 200
|
15
| 10
| 16
| 20
| 1080
| 1800
| 300
|
20
| 12
| 20
| 25
| 1600
| 2400
| 400
|
25
| 15
| 24
| 30
| 2400
| 3750
| 500
|
Solved Examples on Triangular Prism Calculator
1. Find the surface area, volume, and lateral surface area of a triangular prism with a base of sides 6 cm, 8 cm, and 10 cm, and a height of 15 cm.
- A = Area of base + 3 × Area of triangle
- V = Area of base × Height
- P = Perimeter of base × Height
- L = Perimeter of base × Height
Substituting the given values:
Area of base = 1/2 × 6 × 8 = 24 sq. cm
Area of triangle = sqrt(15 × (15 − 6) × (15 − 8) × (15 − 10)) = 72 sq. cm
Perimeter of base = 6 + 8 + 10 = 24 cm
Perimeter of base = 6 + 8 + 10 = 24 cm
Substitute these values into the formulas to get:
A = 24 + 3 × 72 = 240 sq. cm
V = 24 × 15 = 360 cubic cm
L = 24 × 15 = 360 sq. cm
2. Calculate the surface area, volume, and lateral surface area of a triangular prism with a base of sides 4 inches, 6 inches, and 8 inches, and a height of 10 inches.
Following the same formulas:
Area of base = 1/2 × 4 × 6 = 12 sq. in
Area of triangle = sqrt(10 × (10 − 4) × (10 − 6) × (10 − 8)) = 24 sq. in
Perimeter of base = 4 + 6 + 8 = 18 in
Perimeter of base = 4 + 6 + 8 = 18 in
Substituting into the formulas:
A = 12 + 3 × 24 = 84 sq. in
V = 12 × 10 = 120 cubic in
L = 18 × 10 = 180 sq. in
3. Determine the surface area, volume, and lateral surface area of a triangular prism with a base of sides 12 meters, 16 meters, and 20 meters, and a height of 25 meters.
Continuing with the same approach:
Area of base = 12 × 12 × 16 = 96 sq. m
Area of triangle = sqrt(25 × (25 − 12) × (25 − 16) × (25 − 20)) = 120 sq. m
Perimeter of base = 12 + 16 + 20 = 48 m
Perimeter of base = 1/2 + 16 + 20 = 48 m
Substituting into the formulas:
A = 96 + 3 × 120 = 456 sq. m
V = 96 × 25 = 2400 cubic m
L = 48 × 25 = 1200 sq. m
Practice Questions on Triangular Prism Calculator
1. Find the surface area, volume, and lateral surface area of a triangular prism with a base of sides 7 cm, 10 cm, and cm, and a height of 20 cm.
2. Calculate the surface area, volume, and lateral surface area of a triangular prism with a base of sides 5 inches, 12 inches, and 13 inches, and a height of 15 inches.
3. Determine the surface area, volume, and lateral surface area of a triangular prism with a base of sides 9 meters, 12 meters, and 15 meters, and a height of 30 meters.
Conclusion
Triangular prism calculator is a useful tool for quickly finding key measurements like volume and surface area. By inputting the dimensions of the triangular base and the length of the prism, the calculator applies specific formulas to provide accurate results. Mastering the triangular prism calculators provides valuable insights into geometry and real-world applications. With the simple steps outlined in this article, you now possess the knowledge to compute triangular prism properties confidently.
Triangular Prism Calculator - Free Online Calculator – FAQs
What is Triangular Prism Calculator?
A triangular prism calculator serves as a helpful guide for individuals needing to perform manual calculations without depending on tools or software.
Can I use online calculators for finding properties of triangular prisms?
While online calculators offer convenience, understanding manual calculations enhances your understanding of geometry.
Why is it important to know how to calculate properties of triangular prisms?
Understanding geometric concepts like triangular prism properties is essential for fields such as architecture, engineering, and manufacturing.
Are there any shortcuts for finding properties of triangular prisms?
Breaking the triangular prism down into simpler shapes like triangles and rectangles can simplify the calculation process.
Can I use online calculators for finding properties of triangular prisms?
While online calculators offer convenience, understanding manual calculations enhances your understanding of geometry.
Why is it important to know how to calculate properties of triangular prisms?
Understanding geometric concepts like triangular prism properties is essential for fields such as architecture, engineering, and manufacturing.
Are there any shortcuts for finding properties of triangular prisms?
Breaking the triangular prism down into simpler shapes like triangles and rectangles can simplify the calculation process. This method allows you to calculate the properties of individual shapes and then combine them to find the properties of the entire triangular prism.