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101 LearnersLast updated on September 10, 2025
Properties of Triangular Prism
A triangular prism is a three-dimensional shape that has unique properties, making it useful in solving geometric problems involving volume, surface area, and symmetry. A triangular prism consists of two parallel triangular bases and three rectangular lateral faces. These properties are essential for understanding and solving problems related to three-dimensional geometry. Let's explore the properties of a triangular prism in detail.
What are the Properties of a Triangular Prism?
The properties of a triangular prism are straightforward and help students understand and work with this type of three-dimensional shape. These properties are derived from geometric principles. Here are several properties of a triangular prism:
- Property 1: Two Parallel Triangular Bases A triangular prism has two parallel triangular bases that are congruent.
- Property 2: Three Rectangular Lateral Faces The three lateral faces are rectangles, connecting corresponding sides of the two triangular bases.
- Property 3: Edges and Vertices A triangular prism has 9 edges and 6 vertices.
- Property 4: Volume Formula The volume of a triangular prism is calculated using the formula: Volume = Base Area x Height Here, the base area refers to the area of the triangular base, and height is the perpendicular distance between the bases.
- Property 5: Surface Area Formula The surface area of a triangular prism is given by: Surface Area = (Base Perimeter x Height) + (2 x Base Area) Where the base perimeter is the perimeter of the triangular base.
Tips and Tricks for Properties of a Triangular Prism
Students often find it challenging to remember the properties of a triangular prism. To avoid confusion, consider the following tips and tricks:
- Two Triangular Bases: Remember that a triangular prism has two congruent triangular bases that are parallel.Visualizing or drawing the shape can help.
- Rectangular Faces: The three lateral faces are rectangles. This can be easily remembered by noting that they connect corresponding sides of the triangular bases.
- Volume and Surface Area: To find volume, multiply the area of the base by the height. For surface area, remember to include both the lateral surface area and the areas of the two triangular bases.
Confusing with a Rectangular Prism
A triangular prism has triangular bases, whereas a rectangular prism has rectangular bases. Ensure you identify the base shape correctly.
Mistake 1
Misinterpreting the Rectangular Faces
Remember that the lateral faces are rectangles. Each rectangle connects a pair of corresponding sides of the triangular bases.
Mistake 2
Incorrectly Applying the Volume Formula
Ensure you calculate the area of the triangular base correctly. Then multiply it by the prism's height (the perpendicular distance between the bases) to find the volume.
Mistake 3
Overlooking the Surface Area Components
Remember that calculating surface area involves the sum of the lateral surface area and the areas of the two triangular bases. Don't omit any part.
Mistake 4
Confusing Base and Height
In a triangular prism, the base refers to the area of the triangular face, and the height is the distance between the two bases. Don't confuse these terms.
Mistake 5
Solved Examples on the Properties of Triangular Prisms
A triangular prism has a base area of 10 cm² and a height of 5 cm. What is its volume?
Volume = 50 cm³
Problem 1
The volume of a triangular prism is calculated using the formula: Volume = Base Area x Height Substituting the values, we get Volume = 10 cm² x 5 cm = 50 cm³.
A triangular prism has a base perimeter of 12 cm and a height of 6 cm. If the base area is 8 cm², what is its surface area?
Explanation
Surface Area = 88 cm²
Problem 2
Using the surface area formula: Surface Area = (Base Perimeter x Height) + (2 x Base Area) = (12 cm x 6 cm) + (2 x 8 cm²) = 72 cm² + 16 cm² = 88 cm².
How many edges does a triangular prism have?
Explanation
A triangular prism has 9 edges.
Problem 3
A triangular prism is composed of two triangular bases, each with 3 edges, and three rectangular faces, each providing an additional edge, totaling 9 edges.
In a triangular prism, if one of the triangular bases has sides of lengths 3 cm, 4 cm, and 5 cm, what is the perimeter of the base?
Explanation
Perimeter = 12 cm
Problem 4
The perimeter of a triangular base is the sum of the lengths of its sides. Thus, Perimeter = 3 cm + 4 cm + 5 cm = 12 cm.
If the height of a triangular prism is doubled, how does it affect the volume?
Explanation
The volume will also double.
A triangular prism is a three-dimensional shape with two parallel and congruent triangular bases and three rectangular lateral faces.
1.How many faces does a triangular prism have?
2.How do you find the volume of a triangular prism?
3.Are all faces of a triangular prism rectangular?
4.How many vertices are there in a triangular prism?
Common Mistakes and How to Avoid Them in Properties of Triangular Prisms
Students often confuse properties of different geometric shapes, leading to errors.
Here are common mistakes and their solutions when dealing with triangular prisms.
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
