Introduction:-
In geometry, the pentagonal prism is a prism with a pentagonal base.
Pentagonal prism is a type of heptahedron.
If faces are all regular, the pentagonal prism is a semi regular polyhedron and the third in an infinite set of prisms formed by square sides and two regular polygon caps.
A pentagonal prism has Source:- Wikipedia.
7 faces
10 vertices
15 edges.
The pentagonal prism looks like .
Formulas For Pentagonal Prism:-
`Base area = 5/ 2 * a * s`
`Base perimeter = 5s`
`Prisms Surface area = 5as + 5sh.`
`Volume of Prism = (5/2)ash`
`here`
`a = apothem Leng th,`
`s = side,`
`h = height.`
Please express your views of this topic Congruence of Triangles by commenting on blog.
Problems on Prism:-
Problem 1:-
Find the base area and base perimeter of the pentagonal prism if the apothem length is 4 and the side is 2.
Solution:-
Given
The apothem, length is 4
The side is 2.
The formula that is used to calculate the area of the base is `5/ 2 a* s.`
By plugging in the values of a and s in the formula we get
Area of the base = `5/ 2` * 4 * 2.
By crossing 2 and 2 in the above equation we get
Area of the base = 5 * 4 = 20.square units.
The formula that is used to find the base perimeter is `5s` .
By plugging in the given values we get
Base perimeter = 5 * s = 5 * 2 = 10.
Problem 2:-
Find the base area and base perimeter of the pentagonal prism if the apothem length is 6 and the side is 4.
Solution:-
Given
The apothem, length is 6
The side is 4.
The formula that is used to calculate the area of the base is` 5/ 2 a* s.`
By plugging in the values of a and s in the formula we get
Area of the base = `5/ 2 * 6 * 4.`
By crossing 2 and 4 in the above equation we get
Area of the base = 5 * 12 = 60.square units.
The formula that is used to find the base perimeter is `5s.`
By plugging in the given values we get
Base perimeter = 5 * s = 5 * 4 = 20.
Problem 3:-
Find the base area and base perimeter of the pentagonal prism if the apothem length is 5 and the side is .
Solution:-
Given
The apothem, length is 5
The side is 7.
The formula that is used to calculate the area of the base is `5/ 2 a* s.`
By plugging in the values of a and s in the formula we get
Area of the base = `5/ 2 * 5 * 7.`
Area of the base = `175/ 2` square units.
The formula that is used to find the base perimeter is 5s.
By plugging in the given values we get
Base perimeter = 5 * s = 5 * 7 = 35.
In geometry, the pentagonal prism is a prism with a pentagonal base.
Pentagonal prism is a type of heptahedron.
If faces are all regular, the pentagonal prism is a semi regular polyhedron and the third in an infinite set of prisms formed by square sides and two regular polygon caps.
A pentagonal prism has Source:- Wikipedia.
7 faces
10 vertices
15 edges.
The pentagonal prism looks like .
Formulas For Pentagonal Prism:-
`Base area = 5/ 2 * a * s`
`Base perimeter = 5s`
`Prisms Surface area = 5as + 5sh.`
`Volume of Prism = (5/2)ash`
`here`
`a = apothem Leng th,`
`s = side,`
`h = height.`
Please express your views of this topic Congruence of Triangles by commenting on blog.
Problems on Prism:-
Problem 1:-
Find the base area and base perimeter of the pentagonal prism if the apothem length is 4 and the side is 2.
Solution:-
Given
The apothem, length is 4
The side is 2.
The formula that is used to calculate the area of the base is `5/ 2 a* s.`
By plugging in the values of a and s in the formula we get
Area of the base = `5/ 2` * 4 * 2.
By crossing 2 and 2 in the above equation we get
Area of the base = 5 * 4 = 20.square units.
The formula that is used to find the base perimeter is `5s` .
By plugging in the given values we get
Base perimeter = 5 * s = 5 * 2 = 10.
Problem 2:-
Find the base area and base perimeter of the pentagonal prism if the apothem length is 6 and the side is 4.
Solution:-
Given
The apothem, length is 6
The side is 4.
The formula that is used to calculate the area of the base is` 5/ 2 a* s.`
By plugging in the values of a and s in the formula we get
Area of the base = `5/ 2 * 6 * 4.`
By crossing 2 and 4 in the above equation we get
Area of the base = 5 * 12 = 60.square units.
The formula that is used to find the base perimeter is `5s.`
By plugging in the given values we get
Base perimeter = 5 * s = 5 * 4 = 20.
Problem 3:-
Find the base area and base perimeter of the pentagonal prism if the apothem length is 5 and the side is .
Solution:-
Given
The apothem, length is 5
The side is 7.
The formula that is used to calculate the area of the base is `5/ 2 a* s.`
By plugging in the values of a and s in the formula we get
Area of the base = `5/ 2 * 5 * 7.`
Area of the base = `175/ 2` square units.
The formula that is used to find the base perimeter is 5s.
By plugging in the given values we get
Base perimeter = 5 * s = 5 * 7 = 35.
