what is the cross section that is parallel to the base of a triangular prism?
A triangular prism is a polyhedron made up of two triangular bases and three rectangular sides. Information technology is a iii-dimensional shape that has 3 side faces and two base faces, continued to each other through the edges. If the sides are rectangular, then it is called the right triangular prism else it is said to exist an oblique triangular prism. If the bases are equilateral and sides are squares, and then it is called a uniform or regular triangular prism. Like other Prisms , the two bases here are parallel and coinciding to each other. In total, it has five faces, vi vertices and 9 edges.
What is a Triangular Prism?
Triangular Prism is a pentahedron and has 9 distinct nets . The edges and vertices of the bases are joined with each other via three rectangular sides. The sides of the triangular prism, which are rectangular in shape are articulation with each other side past side. All cross-sections parallel to the base faces are the same equally a triangle. A triangular pyramid has four triangular bases dissimilar the triangular prism, joined with each other and all are congruent to each other.
The sides and bases of the triangular prism are congruent or else oblique. The edges of the prism join the corresponding sides. The two bases of this prism are equilateral triangles and the edges of these triangles are parallel to each other. See the below figure to understand the structure.
Other Types of Prisms
- Rectangular Prism
- Foursquare prism
- Pentagonal Prism
Properties of Triangular Prism
Permit the states discuss some of the backdrop of the triangular prism.
- Information technology has a total of 9 edges, 5 faces, and 6 vertices (which are joined by the rectangular faces).
- It has ii triangular bases and three rectangular sides
- If the triangular bases are equilateral and the other faces are squares, instead of a rectangle, then the triangular prism is said to exist semiregular
Right Triangular Prism
A right triangular prism has its three rectangular sides coinciding. Besides, the two triangular bases are parallel and coinciding to each other. The rectangular or lateral faces are perpendicular to the triangular bases.
Volume of Triangular Prism
The volume of a triangular prism is equal to the product of the triangular base area and the height of the prism. The formula to discover the volume of triangular prism is given by:
Volume = Area of the Base × Height of prism
Since, the base is in triangular shape, therefore,
Area = ½ b h
Hence,
Book of Triangular Prism = ½ × b × h × l
Where b is the base of operations length, h is the top of the triangle and l is the length between the triangular bases.
Surface Area of Triangular Prism
Surface area of triangular prism is equal to the sum of the lateral surface area and twice the base of operations area of the triangular prism. It is measured in square units. The formula of surface area of triangular prism is given past:
Surface area of triangular prism = 2A + PH
Where,
- A is the area of the triangular bases,
- P is the perimeter of the bases and
- H is the height of the prism
Now, Area of the triangular base= ½ × b × h
If a, b and c are the sides of the triangular bases, and so,
Perimeter of the base = a + b + c
Therefore,
Surface surface area of triangular prism = 2 (½ × b × h) + (a + b + c)H
Surface Expanse of the Triangular Prism = (bh + (a + b + c)H)
Where b and h is the base and height of the bases, respectively and H is the pinnacle of the prism.
Triangular Prism Net
If we open each confront of the triangular prism, we will get the net. The cyberspace of this prism comprises three rectangles and two triangles. In the below figure you tin can see the nine distinct nets.
Facts to Remember
- Number of faces = 5
- Number of edges = nine
- Number of vertices = 6
- Shape of the base = Triangular
- Shape of Sides = Rectangular or Square
- Surface Expanse = 2(Expanse of triangular bases) + Perimeter of base 10 Height of prism
- Book = Area of base x Acme of Prism
Related Articles
- Expanse Of prism
- Volume of a Prism
Solved Examples on Triangular Prism
Example 1: Find the volume of the triangular prism with base is 5 cm, top is ten cm, and length is xv cm.
Solution: Volume of Triangular Prism = ½ × b × h × l
V = ½ × 5 × x × 15
Volume, V = 375 cm3
Example 2: If the height of the prism is 4cm and the length of the side of the equilateral triangular base of operations is 6cm. Then detect the expanse of the prism for the in a higher place example.
Solutions: We have,
Base = 5cm, superlative of the base= 10cm, length of the base=15cm, Height of the prism = 4cm
As the base of operations is an equilateral triangle, therefore all its sides will exist equal.
Hence, a = b = c = 6cm.
By the formula,
Surface area of the Triangular Prism = (bh + ( a + b + c)H)
Area = (five × x + (half dozen + 6 + half dozen)4)
=(50 + (18)four) = l + 72
= 122 cm2
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Often Asked Questions on Triangular Prism
What is a triangular prism?
A triangular prism is polyhedron and a three-dimensional shape that has 5 faces, vi edges and 9 vertices. Its bases are triangular and sides are rectangular.
How many faces, edges and vertices a triangular prism has?
A triangular prism has five faces (3 rectangular and 2 triangular), 9 vertices and vi edges.
What is the formula to detect the book of a triangular prism?
The formula to find book of triangular prism is the product of expanse of triangular base of operations and height of prism.
Volume = ½ × b × h × fifty
What is the surface surface area of a triangular prism?
Surface area of triangular prism is the total expanse covered by its surface in three dimensional airplane. The formula is given by:
Expanse = bh + ( a + b + c)H
Where a, b and c are the sides of triangular bases and H is the height of the prism.
What is the difference between triangular prism and rectangular prism?
A triangular prism has its bases in triangle shape and a rectangular prism has its bases in rectangle shape.
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