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Prism

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Understanding Prism Shapes: Types, Definitions, and Relationships with Pyramids

Comprehensive Definition, Description, Examples & Rules 

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Introduction

A prism is a solid shape with two ide­ntical flat ends, which can be in the shape of a square, triangle, or rectangle­. These flat ends, such as a triangular or square prism, determine the prism type. Unlike curved shape­s, prisms have straight lines connecting all sides and are considered closed shapes. They are solid shapes covered on all side­s by flat surfaces called faces. The­ top and bottom faces of the prism are ide­ntical and referred to as its base.

Importance in Geometry

The primary importance of the prism in geometry is:

  • It is a major member of the polyhedron family and has a congruent polygon in its top and base.
  • Apart from the prism’s top and bottom base, the other face of the prism is known as the lateral face. 
  • A prism is a shape that does not consist of a curved shape.
  • It consists of a cross-sectional figure across all its length. 

What is a Prism?

If you’re to define prism, it is a three-dimensional shape with two identical e­nds at the top and bottom. It is made up of flat faces with e­qual cross-sectional lengths. The faces of the prism can be either rectangles or parallelograms, depending on their base shape. For example, a triangular prism consists of three rectangular surfaces and two triangular faces angled together. Anothe­r prism is formed by a square and a re­ctangle as its base, known as a square or re­ctangular prism. Prisms are transparent solid bodies with spe­cific geometric properties. 

Characteristics

The fundamental characteristics of a Prism are:

  • It consists of a solid shape with two identical ends: a rectangle, square, or triangle.
  • Another characteristic is that it consists of all flat surfaces and straight lines, and a Prism does not consist of any curved surface. 
  • It has a cross-sectional that looks like a triangle, square, or rectangle according to its base. 

Polyhedron

A polyhedron is any thre­e-dimensional shape with flat polygonal face­s and sharp corners formed by straight edge­s. One example of a polyhe­dron is a prism with a flat polygonal face as its base (such as a triangle, re­ctangle, or square). These characteristics classify the prism as a type of polyhe­dron.

Prism Shape and Features

The shape of a Prism is a solid 3D figure consisting of two similar ends at the top and bottom, directly relating to a rectangle, square, or triangle. A prism is a flat face with flat surfaces and uniform cross-sectional lines. The prism shape can be considered a polyhedron, a three-dimensional shape with essential geometry properties.

Geometric Properties

The defining geometric properties of a Prism are:

  • It consists of two identical ends, which is the major property of the prism according to geometry. 
  • In geometry, a prism can be considered a polyhedron comprising several polygonal bases and polygonal faces, which is important for a parallelogram. 
  • All the sides and lengths of the prism are straightened. It does not consist of a curve angle.
  • A Prism consists of two parallel bases, known as two parallel congruent faces of the prism. These two parallel bases at the top and bottom are identical, rectangular, triangular, or square-shaped. The type of the prism’s base determines the exact type of prism. The parallel bases are joined with rectangular or parallelogram faces, considered the prism’s lateral faces. 

Right Prism

A right Prism is considered a solid 3D object that consists of two parallel bases of the same shape and several rectangular faces depending upon the shape of the bases. One of the characteristics of the right prism is that its bases and all its rectangular faces directly meet at a perpendicular line that connects at 90 degrees or right angles. 

All the opposite faces of the right prism are congruent, and the bases being perpendicular to the lateral faces make it a right-angle prism known as the right prism.

Types of Prism

A prism can be classified into different types according to the identical shape of its bases. The type of base has to determine the type of prism. The types of prisms are:

Triangular Prism

Triangular prisms are a frequently encountered type of prism that have triangles on both e­nds. They have a total of five faces, with two being triangular bases and the­ remaining three being rectangular faces called lateral faces.

Pentagonal Prism

A pentagonal prism consists of two pentagonal bases at the bottom and top of the prism. It consists of the remaining five rectangular sides, making it a pentagonal prism, which is the heptahedron. One of the characteristics of a pentagonal prism is that it consists of a total of 15 edges. 

Rectangular Prism

Another common prism shape is a rectangular prism, which consists of two congruent bases in a rectangle shape. A rectangular prism consists of a total of eight vertices and six faces with a total of twelve edges. Out of the six faces of the rectangular prism, two are the rectangular base, while the remaining four are the lateral faces of the rectangular prism.

Prism and Pyramid Relationship

One important re­lationship in geometry exists between prisms and pyramids. When a prism and pyramid have the same height and base, the volume of the pyramid is one­-third of the volume of the prism. Additionally, a prism and a pyramid have lateral faces, with the triangular prism directly related to a triangular pyramid based on their shared base. 

There are major differences between a pyramid and a Prism, as a pyramid consists of triangular lateral surfaces while a Prism consists of rectangular lateral faces. Similarity among both the shapes is that both the lateral faces of the prism and the pyramid are angled towards the base, or in terms of the prism, it is the base. 

Practical Applications of Prisms

There are many areas in the real world where you can find prisms. These are:

  • Buildings: Many architects use the prism shape to build buildings. The buildings have similarities, making them an important property of construction and architecture. 
  • Chocolate Bar: A chocolate bar can be considered an example of a Prism as its features make it one of the prism shapes with certain faces and bases.
  • Box: A box can be of the prism shape, and it is one of the everyday objects you use that is a Prism shape. 

Applications of the Prism:

  • Architecture: The area in which the prism is used is the architectural field as a construction. Architecture is where most geometrical shapes play a huge part, and prism is one of the shapes where you want to build your buildings in that manner. 
  • Engineering: Engineering and architecture have similarities and have been an important part of the real world. Engineers, especially civil engineers, use the presumption shape to build bridges and roads. 
  • Everyday Objects: As mentioned earlier, everyday objects like a chocolate bar or a box are considered a Prism shape and have major similarities with the Prism. 

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Key Takeaways

  1. A prism is considered to be a Polyhedron Shape.

  2. The top and the bottom bases of the prism are identical to each other. 

  3. There is a great relationship between the prism and pyramid as it has certain similarities and differences.

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Frequently Asked Questions

The formula to calculate the total surface area of a particular prism is:

  • S = (2 × Base Area) + (Base Perimeter × Height)

It is a formula that makes calculating all sorts of prisms possible. 

The formula to calculate the total volume of a Prism is:

  • V = Area of Base × Height of Prism

The calculation for the irregular prism will mean that the irregular polygons will be there in the bases of the prism. It means an irregular prism will have different angles, and the sides will not be equal. The base area will be different, but the formula to calculate the volume of the irregular prism will be the same as the regular prism, which is the base area multiplied by the height. 

There are no uncommon types of prisons as any polygonal base can be formed under the prism, and the common examples of a Prism are:

  • Square prism
  • Rectangular Prism
  • Triangular Prism
  • Octagonal Prism
  • Pentagonal Prism

A right prism is a unique type of prism that is a solid 3D object, and the rectangular faces meet at the perpendicular line that directly connects at 90 degrees, making it a right angle so the prism is known as a right prism. 

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2D Shapes2cosacosb Formula30-60-90 Formulas3D ShapesAbsolute Value FormulaAcute AngleAcute Angle triangleAdditionAlgebra FormulasAlgebra of MatricesAlgebraic EquationsAlgebraic ExpressionsAngle FormulaAnnulusAnova FormulaAnti-derivative FormulaAntiderivative FormulaApplication of DerivativesApplications of IntegrationArc Length FormulaArccot FormulaArctan FormulaArea Formula for QuadrilateralsArea FormulasArea Of A Sector Of A Circle FormulaArea Of An Octagon FormulaArea Of Isosceles TriangleArea Of ShapesArea Under the Curve FormulaArea of RectangleArea of Regular Polygon FormulaArea of TriangleArea of a Circle FormulaArea of a Pentagon FormulaArea of a Square FormulaArea of a Trapezoid FormulaArithmetic Mean FormulaArithmetic ProgressionsArithmetic Sequence Recursive FormulaArithmetic and Geometric ProgressionAscending OrderAssociative Property FormulaAsymptote FormulaAverage Deviation FormulaAverage Rate of Change FormulaAveragesAxioms Of ProbabilityAxis of Symmetry FormulaBasic Math FormulasBasics Of AlgebraBinary FormulaBinomial Probability FormulaBinomial Theorem FormulaBinomial distributionBodmas RuleBoolean AlgebraBusiness MathematicsCalculusCelsius FormulaCentral Angle of a Circle FormulaCentral Limit Theorem FormulaCentroid of a Trapezoid FormulaChain RuleChain Rule FormulaChange of Base FormulaChi Square FormulaCirclesCircumference FormulaCoefficient of Determination FormulaCoefficient of Variation FormulaCofactor FormulaComplete the square formulaComplex numbersCompound Interest FormulaConditional Probability FormulaConeConfidence Interval FormulaCongruence of TrianglesCorrelation Coefficient FormulaCos Double Angle FormulaCos Square theta FormulaCos Theta FormulaCosec Cot FormulaCosecant FormulaCosine FormulaCovariance FormulaCubeCurated Maths Resources for Teachers – EdulyteCylinderDecimalsDifferential calculusDiscover the world of MathsEllipseEquilateral triangleEuler’s formulaEven numbersExponentsFractionFraction to decimalGeometric sequenceHeptagonHyperbolaIntegersIntegrationIntegration by partsLinesLocusMatricesNatural numbersNumber lineOdd numbersParallelogramPercentage formulaPerimeterPolygonPolynomialsPrismProbabilityPyramidPythagoras theoremRoman NumeralsScalene triangleSetsShapes NamesSimple interest formulaSlope formulaSolid shapesSphereSquareStandard deviation formulaSubtractionSymmetryTimeTrianglesTrigonometry formulaTypes of anglesValue of PiVariance formulaVectorVolume formulasVolume of a coneVolume of sphere formulaWhole numbers
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