How to Find the Surface Area of a Prism

What is a Prism

A prism is a polyhedron, in which is a solid object consisting of two congruent (similar in shape and equal in size) polygonal faces with their identical edges connected by rectangles. The polygonal face is known as the base of the prism, and the two bases are parallel to each other. However, it is not necessary that they are exactly positioned above each other. If they are positioned exactly above each other, then the rectangular sides and the base meets at right angles, then, the prism is known as a right-angled prism.

How to find the surface of a prism|

Any of these shapes can be referred to as a prism.

How to find the surface area of a prism: Method

A prism contains at least 5 surfaces. Moreover, if the prism is irregular, most likely the area of each surface has to be calculated separately and has to be added to get the total surface area. Nevertheless, in a regular prism with familiar geometry this problem is a little simpler.

Prism has two base surfaces and n number of rectangles connecting these surfaces. In some cases, the shape is irregular, and the area varies from one surface to another. Then, we can find the area of the prism by following formula.

Total Area=2[Area of the Base]+[Area of all Sides, the Rectangles]

If the bases are a regular polygon, the sides or the rectangles become similar and same in size. Therefore, it is enough to calculate the area of a single base and the area of a single rectangle. Assuming a regular prism geometry and for a n sided polygon as the base, the total area becomes.

Total Area=2[Area of the Base]+n[Area of a Side, the Rectangle]

Triangular prisms are the commonly used type of prisms, and considering an equilateral triangular prism with we can modify the above formula into,

Total Area of a Triangular Prism=2[1/2 ah]+3[al]

Where the length of a side of the prism is l, h is the perpendicular height of the triangle with side a.

How to find the surface area of a prism: Example

  1. A prism has a cross-sectional area of an equilateral triangle with 3cm sides. If the prism is 10cm long find the total area of the prism.
    • Find the area of the base

Base is an equilateral triangle with 3cm. Therefore, the area of the triangle is,

How to find the surface of a prism |

    • Find the area of a side.

A side is rectangular in shape and 10cm in length and 3cm in width, therefore, the area of a single side,

How to find the surface area of a prism |

    • There are 3 sides and two bases in a triangular Prism, therefore, the total area of the prism is,

How to find the surface area of a prism |

About the Author: admin

Leave a Reply

Related pages

pouring fondant icingdarwin vs lamarckmetallic and nonmetallic mineral resourcesdifference between llamas and alpacascyst tumor differencedefinition of hallucination in psychologyleukocytes vs lymphocytesorganism with bilateral symmetryfuchsia and magenta differenceaffix and suffixchlorophyll vs chloroplastdifference between intramolecular and intermolecular forcescolloid fluid definitionwhat is the relationship between monomers and polymerswhat is the difference between a peasant and a serffondant vs gum pasteactivity based costing method examplewhat is soliloquy in dramadistinguish between infrasound and ultrasound wavesgram pos vs gram nega refrain in poetrychemical composition of formaldehydeexamples of homogeneous mixtures in chemistryequilibrium price and quantity formuladefine the term valence shelldefinition for sister chromatidsthe difference between intermolecular and intramolecular forcesstatic friction vs kinetic frictioneubacteria habitatpredicate nomitivedefinition of tardive dyskinesiatheft vs larcenybasal energy expenditure and resting energy expenditurecellulose versus starchpictures of common nouns and proper nounswhat is the difference between manic depressive and bipolaramylose chemical formuladifference centripetal and centrifugal forcewhats the difference between calzone and strombolidifference between low density and high density polyethylenedifference between idioms and phrasesaldehydes vs ketonesbaking soda and bicarbonate of sodaexplain the difference between hiv and aidsfunction of basophils and eosinophilsdifference between reflection and refractionpixies fairies and spritestensile strength at yielddying vs dieingwhat is the difference between a voltmeter and an ammetermorph morpheme allomorphdiamante poem antonymphrases and clauses examplesthe difference between a cyclone and a tornadoinduction and orientation ppttyphoon hurricane differencenicknames for dachshundswhat is the difference between recessive and dominantis bicarbonate soda the same as baking sodanomadic life definitiondifference between monocot and dicot leafdefine prophase 1patronize exampleexample of carpe diemdifference between nitrite and nitrateis albinism a mutationprincipal of conservation of linear momentumpolythene thermosetting or thermoplasticsubject predicate example sentencestransnational corporation meaningdefine round character in literaturethymine cytosinesister chromatids definitioncoriander vs cilantro vs parsleydifference between primary and secondary successionrose homophone