Pentagonal Prism Surface Area Calculator

A pentagonal prism is a prism that has two pentagonal bases like top and lesser and five rectangular sides. It is a type of heptahedron with vii faces, 10 vertices and 15 edges. A pentagonal prism can have pentagonal bases which give v sides. A pentagonal prism is also known equally a five-sided polygon prism.

To recall, the prism shape, in maths, is a three-dimensional box i.e. a solid figure with a compatible cross-department and has two common bases.

Face: A apartment side of a 3-dimensional object
Base: One of the two parallel and coinciding sides of an object
Edge: Intersection of two faces on a solid object. This is a line.
Vertex: Joining point of ii border sides.

Types of Pentagonal Prisms

There are two types of pentagonal prisms which are:

Regular Pentagonal Prisms
Correct Pentagonal Prisms

Regular Pentagonal Prism

If all the sides of the pentagonal prism are of equal length, then information technology is said to be a regular pentagonal prism. In a regular pentagonal prism, all the rectangular faces are congruent. The rectangular faces are said to be lateral when the pentagonal faces of the regular pentagonal prism are bases. The lateral side faces are called lateral edges.

Rectangular Pentagonal Prism

A prism is a right pentagonal prism when it has two coinciding and parallel pentagonal faces and five rectangular faces that are perpendicular to the triangular ones.

Volume and Surface Area of a Pentagonal Prime

The two of import measures made on a pentagonal prism are to find its volume and surface surface area.

Pentagonal Prism

Volume of Pentagonal Prism Formula

To find the book of a regular pentagonal prism, beginning, yous have to find the apothem length (a). The apothem length is a measure from the centre of a polygon to the midpoint of any side. The formula to find the volume of a pentagonal prism is given as:

Volume of pentagonal prism= (5/ii)×a×b×h cubic units

Where,

a = Apothem length of the pentagonal prism
b = Base of operations length of the pentagonal prism
h = Height of the pentagonal prism

Learn More than: Volume of a Prism

Surface area of Pentagonal Prism Formula

The surface area is the area that describes the material that volition be used to comprehend a geometric solid shape. The formula to find the surface area of the pentagonal prism is given by:

Surface surface area of pentagonal prism = 5ab + 5bh square units

Where,

a = apothem length of the pentagonal prism
b = base length of the pentagonal prism
h = height of the pentagonal prism

Learn More: Area Of a Prism

Case Question Based on Pentagonal Prism Formulas

Question: Find the surface area and volume of the pentagonal prism with apothem length of six cm, base length of x cm and height of 11 cm?

Solution:

Given,

Apothem Length of the pentagonal prism, a = 6 cm

Base length of the pentagonal prism, b = 10 cm

Tiptop of the pentagonal prism, h = eleven cm

Volume and the expanse of a pentagonal prism

Volume of the pentagonal prism = (5/ii)abh cubic units

= 5/two × (six×ten×11)

= v/2 × (660)

= 5 × 330

= 1650

Therefore, the volume of the pentagonal prism is 1650 cm³

Surface expanse of pentagonal prism = 5ab + 5bh square units

= 5 (6×10) + 5 (10×xi)

= 5(60) + v(110)

= 300 + 550

= 850

Therefore, the surface area of a pentagonal prism is 850 cmⁱⁱ.

Oftentimes Asked Questions

What is Prism?

A prism can be divers equally a three-dimensional shape that consists of 2 parallel, congruent faces called bases.

What is a Pentagonal Prism?

A pentagonal prism can be divers as a prism having two pentagonal bases and five rectangular sides.

What is the Formula for Surface Expanse of a Pentagonal Prism?

The surface surface area of a pentagonal can be found using the post-obit formula:

A = 5ab + 5bh

What is the Formula for the Book of a Pentagonal Prism?

The volume of a pentagonal prism can be calculated using the post-obit formula:

V = (five/ii)×a×b×h