What is the surface area formula for a trapezoidal prism?

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Answer 1 · 2018-04-20T17:27:59

#S = a(h + l) + b(h + l) + cl + dl#

Given: a trapezoidal prism

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The base of a prism is always the trapezoid for a trapezoidal prism.

The surface area #S = 2*A_(Base) + "Lateral Surface Area"#

#A_(trapezoid) = A_(Base) = h/2 (a + b)#

#L = "Lateral Surface Area"# = the sum of the areas of each surface around the Base.

#L = al + cl + bl + dl#

Substitute each piece into the equation:
#S = 2*h/2 (a + b) + al + cl + bl + dl#

Simplify:
#S = h(a + b) + al + cl + bl + dl#

Distribute and Rearrange:
#S = ha +hb + al + cl + bl + dl#

#S = a(h + l) + b(h + l) + cl + dl#