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surface area of the triangular prism

by Frank Hernandwez
(NYC)











































triangular prism - surface area

Complete each step using the formula surface area equals two times b plus p times h to find the surface area of the triangular prism.

A triangular prism is shown that has base nine meters, height twelve meters, slant height fifteen meters, and width of six meters.

a. Explain in words what each variable in the formula represents.

B represents __________.

P represents __________.

H represents __________.


b. Find B.

c. Find P.

d. Find H.

e. Find SA.

Comments for surface area of the triangular prism

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Apr 21, 2014
triangular prism
by: Staff


Answer

Part I

According to your problem statement, the formula for the surface area of a triangular prism is:

SA (surface area) = 2b + ph



Triangular prism surface area calculation





Since you did not include a diagram with your question, I'm going to use the following diagram:



Triangular prism







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Apr 21, 2014
triangular prism
by: Staff


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Part II


p = base perimeter = S₁ + S₂ + S₃

h = length of prism = L

b = base area of one end of the prism (area of the triangle with sides S₁-S₂-S₃)


Triangular prism 

find

      p:  base perimeter

      h:  length of prism

      b:  area of base





The known dimensions of the prism are:

S₁ = 15 m

S₂ = 12 m

S₃ = 9 m

L = 6 m



Triangular prism showing dimensions

sides

      S₁ = 15 m 

      S₂ = 12 m

      S₃ = 9 m

      L = 6 m 

*** Click to enlarge image ***






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Apr 21, 2014
triangular prism
by: Staff


-----------------------------------------------


Part III


The two unknown values which are used in the formula for the surface area are:

p = unknown

b = unknown


the value of p can be calculated as follows:

p = base perimeter = S₁ + S₂ + S₃

p = 15 + 12 + 9 = 36 m


Triangular prism - calculating the base perimeter

*** Click to enlarge image ***





The area "b" can be calculated using "Heron's Formula"

"Heron's Formula" can be used to calculate the area of any triangle when the length of each side is known


b = √[s(s - S₁)(s - S₂)(s - S₃)]



Triangular prism - calculate the area of the base using Heron's formula 

*** Click to enlarge image ***







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Apr 21, 2014
triangular prism
by: Staff


-----------------------------------------------


Part IV


the value of "s" (the small s) is equal to half of the triangle's perimeter

s (small s) = ½ * (S₁ + S₂ + S₃)

s = ½ * (15 + 12 + 9)

s = ½ * (36)

s = 18

the value of b can now be calculated as:

b = √[s(s - S₁)(s - S₂)(s - S₃)]

b = √[18 (18 - 15)( 18 - 12)( 18 - 9)]

b = √[18 (3)( 6)( 9)]

b = √(2916)


b (area of one end) = 54 m²



 Triangular prism - calculating the area of the base 

*** Click to enlarge image ***




The total Surface Area (SA) of the triangular prism can now be calculated using the formula listed in the problem statement:


SA (surface area) = 2b + ph

b = 54 m²

p = 36 m

h = 6 m

SA = 2 * 54 + 36 * 6

SA = 108 + 216

SA = 324 m²



 Triangular prism - calculating the total surface area 

*** Click to enlarge image ***






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Apr 21, 2014
triangular prism
by: Staff


-----------------------------------------------


Part V



the final answer is:

the surface area of the triangular prism is: 324 m²


 Surface Area of the triangular prism - final answer

*** Click to enlarge image ***





you can verify the accuracy of the final answer using the following on-line calculator:

Surface Area of Triangular Prism - on-line Calculator





Thanks for writing.

Staff
www.solving-math-problems.com



May 30, 2015
please answer this!!!!!!!!!!!!!!!!!!!
by: Anonymous

hi!!!!!!!! lol

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