Let's calculate the area of the trapezoid shown b1 and b2 are the parallel bases; h is the height of the 2D trapezoid b1 = 2 b2 = 5 h = 1.5
A = h*(b1+b2)/2 A = 1.5*(2+5)/2 A = 1.5*7/2 A = 10.5/2 A = 5.25 The area of one 2D trapezoid is 5.25 sq cm There are two of these trapezoids that form the base faces of the trapezoidal prism. So the total base area is 2*5.25 = 10.5 sq cm Keep this value (10.5) in mind. We'll use it later.
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Now onto the lateral surface area (LSA) It turns out that the formula for the LSA is LSA = p*d where p = perimeter of the trapezoid shown d = depth or height of the 3D trapezoid (I'm not using h as it was used earlier) This formula works for any polygonal base. It doesn't have to be a trapezoid.
In this case the perimeter is, p = 1.7+2+2.65+5 p = 11.35
So LSA = p*d LSA = 11.35*10 LSA = 113.5
Add this LSA to the base area found earlier 10.5+113.5 = 124
