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:
$S = ha +hb + al + cl + bl + dl$

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