# 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

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

 Apr 21, 2014 triangular prism by: Staff ----------------------------------------------- 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) The known dimensions of the prism are: S₁ = 15 m S₂ = 12 m S₃ = 9 m L = 6 m -----------------------------------------------

 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 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)] -----------------------------------------------

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

 Apr 21, 2014 triangular prism by: Staff ----------------------------------------------- Part V the final answer is: the surface area of the triangular prism is: 324 m² 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