how to find the volume of a triangular prism
Volume of Triangular Prism
The book of a triangular prism is the space occupied by it from all three dimensions. A prism is a solid object which has identical bases, apartment rectangular side faces, and the same cantankerous-section all along its length. There are dissimilar types of prisms that are classified and named equally per the shape of their base. A triangular prism has 2 identical triangular bases and 3 rectangular lateral faces.
| ane. | What is the Volume of a Triangular Prism? |
| ii. | Book of Triangular Prism Formula |
| 3. | How to find the Volume of Triangular Prism? |
| 4. | FAQs on Book of Triangular Prism |
What is the Volume of a Triangular Prism?
The volume of a triangular prism tin exist calculated by taking the production of the area of the triangular base of operations and the height of the prism which is also known as the length of the prism. For this, let us first empathize what a triangular prism looks like.
Definition of Triangular Prism
A triangular prism is a polyhedron made up of two triangular bases and three rectangular sides. Or, it tin be considered as a pentahedron (as it has 5 faces altogether) wherein the edges and vertices of the bases are joined with each other past three rectangular sides. By definition, the ii triangular bases are parallel and coinciding to each other. Information technology has:
- 2 bases (which are congruent triangles)
- three side faces (which are coinciding rectangles)
- Total number of faces - v
- 9 edges
- six corners or vertices
The length of the triangular prism is the perpendicular distance between the centers of the two bases. It is represented by "50" in the figure given below.
Observe the triangular prism shown to a higher place where 'b' is the base of each side of two congruent triangles, 'h' is the height of the base triangle, and 'l' is the length of the prism.
Book of Triangular Prism Formula
The volume of a triangular prism is the infinite inside it or the space occupied by it. Information technology is measured in cubic units such as cm3, mthree, in3, etc. We will run into the formulas to summate the volumes of dissimilar types of triangular prisms. The volume of any prism is obtained past multiplying its base of operations area by its length.
The volume of a prism = base of operations surface area × length of the prism
Nosotros will use this formula to calculate the volume of a triangular prism too. We know that the base of a triangular prism is a triangle. By applying the above formula to a triangular prism, we get,
Book of a triangular prism = expanse of base triangle × length of the prism
Here, we can discover the area of the base triangle based on its type and the available information. The post-obit listing shows the formulas to find the area of the base of operations triangle.
- If the base of operations triangle is an equilateral triangle (in this case, the prism is called equilateral triangular prism) with each side 'a', and then its area = √3aii/4
- If the triangle'due south base 'b' and top 'h' are given, and so its surface area = (1/ii) bh
- If the base triangle is a right-angled triangle (in this case, the prism is chosen a right triangular prism) with two legs 'b' and 'h' then its surface area = (ane/2) bh
- If the base of operations triangle is an isosceles triangle with its sides to be 'a', 'a', and 'b' then its area is (b/iv) × √(4a2 - b2)
- If the base triangle is a scalene triangle where all 3 sides 'a', 'b', and 'c' are given, then its area is calculated using √[s(s-a)(s-b)(s-c)]; where, s = (a + b + c)/2. Note that y'all tin can utilize this formula (which is also chosen Heron's formula) for an isosceles triangle (or) an equilateral triangle as well.
- If the base triangle'southward two sides 'a' and 'b' and the included angle 'θ' are given, then its surface area is plant using 1/ii ab sin θ
How to Detect the Volume of Triangular Prism?
The volume of a triangular prism tin exist calculated with the help of the following steps and the case given below. Before that make sure that all measurements are of the same units.
- Step 1: Identify the blazon of the base triangle and notice its surface area using a suitable formula (as explained in the previous department).
- Step ii: Place the length of the prism (Note that this length of the prism is as well known as the height of the prism, and it should not be confused with the height of the base triangle).
- Pace 3: Multiply the base area (from step i) and the length of the prism to detect the volume.
Instance: Calculate the book of the triangular prism whose length is 15 in and whose base is an equilateral triangle of side half dozen inches.
Solution: The volume of the triangular prism tin be calculated using the following steps.
- Stride i: The base triangle is an equilateral triangle with its side as a = six. So its area is found using the formula, √3a2/4 = √3(6)ii/four = ix√3 square inches.
- Footstep 2: The length of the prism is 15 in.
- Footstep three: The volume of the given triangular prism = base of operations surface area × length = ix√3 × 15 = 135√3 cubic inches.
Tips on Volume of Triangular Prism
- The length of a triangular prism is as well known as the peak of the prism.
- This height of the prism should not be confused with the elevation of the base triangle.
☛ Related Manufactures
- Volume of 3D Shapes
- Volume of Cube
- Volume of Cylinder
- Volume of Cuboid
- Book of Sphere
- Book of Rectangular Prism
Examples on Volume of Triangular Prism
-
Example 2: Find the book of the following correct triangular prism.
Solution:
The base of operations of the triangle (b) = 14 ft, and its pinnacle (h) = 8 ft.
So the base of operations surface area = (ane/2) × (bh) = (1/2) × (14 × viii) = 56 square feet.
The length of the prism is, L = 10 ft.
Using the volume of the triangular prism formula,
The book of the given triangular prism = base of operations area × length of the prism = 56 × 10 = 560 ftthree.
go to slidego to slidego to slide
Have questions on bones mathematical concepts?
Get a problem-solving champ using logic, not rules. Learn the why behind math with our Cuemath'south certified experts.
Book a Free Trial Course
Practice Questions on Volume of Triangular Prism
go to slidego to slide
FAQs on Book of Triangular Prism
What is the Volume of Triangular Prism?
The book of a triangular prism is the infinite inside it. It is calculated past multiplying the area of the triangular base and the height of the prism which is also known equally the length of the prism. The volume of a triangular prism is expressed in cubic units such as cmiii, chiliadiii, in3, etc.
What is the Formula for Finding the Book of Triangular Prism?
The formula to notice the volume of a triangular prism is, Volume = base area × length, where,
- Base of operations area = expanse of the base (which is a triangle)
- Length = length of the triangular prism (also known as the meridian of the prism)
How to Find the Height of a Triangular Prism with the Book?
The height of a triangular prism is also known equally the length of the prism. Information technology can be calculated if the base of operations area and the volume of the prism is known. The formula for the volume of a triangular prism = Base area × length of the prism. From this, the top of a triangular prism is obtained by dividing its volume by its base area.
How to Find Book of Triangular Prism with Right Bending?
If the base of a triangular prism is a right-angled triangle of base 'b' and elevation 'h' and the length of the prism is 'Fifty", then its base of operations area = (one/ii) bh. We know that the volume of the prism = base expanse × Length of the prism. Therefore, the volume of the prism, in this case, is calculated using the same formula, Volume of triangular prism = (1/2) bh × L.
What is the Formula to Summate the Volume of an Equilateral Triangular Prism?
Consider a triangular prism whose length is 'L' and whose base is an equilateral triangle of side 'a'. And so its base area is √3a2/4. We know that the volume of the prism = base surface area × length of the prism, hence, the volume of the prism, in this case, is found using the formula (√3a2 × 50)/4
How to Find the Book of a Triangular Prism with an Angle Given?
Consider a triangular prism whose length is 'L' and 'a' and 'b' are the two sides of its base of operations with an included angle θ. Then its base area is (i/two) ab × sin θ. Nosotros know that the volume of the prism is base area × length of the prism, hence the book of the prism, in this instance, is institute using the formula (one/2) ab sin θ × L.
How is the Area of a Triangle Related to the Volume of a Triangular Prism?
The expanse of a triangle is used to observe the volume of a triangular prism because the base of a triangular prism is a triangle and the formula that is used to find the volume of a triangular prism is, Volume = base expanse × length of the prism, where the base of operations area is the area of the triangle. The formula to detect the volume of a triangular prism is, Volume = base area × length of the prism, which shows the relationship between the surface area of a triangle.
Source: https://www.cuemath.com/measurement/volume-of-a-triangular-prism/
Posted by: haneywhick1943.blogspot.com
0 Response to "how to find the volume of a triangular prism"
Post a Comment