Problem:

What is the solution and the formula of the given surface area if the answer is 176.4cm ²?

Surface area shape: trapezoidal prism

Solution:

by manual calculation

get the area of each shape then get the total sum of areas

A1, A2, A3, A4 are rectangular shapes

A5 and A6 are the trapezoidal shapes

Surface Area = A1 + A2 + A3 + A4 + A5 + A6

Surface Area = 10(7) + 3.6(7) + 3.6(7) + 4(7) + (2)((10 + 4)/2) +  (2)((10 + 4)/2)

Surface Area = 70 + 25.2 + 25.2 + 28 + 14 + 14

Surface Area = 176.4 cm²

by using formula

get the perimeter of the trapezoid

Perimeter = 4 + 3.6 + 3.6 + 10

Perimeter = 21.2 cm

get the area of the trapezoid

Base B = 1/2(2)(10 + 4)

Base B = 14 cm²

Surface Area = Perimeter(height) + 2(B)

Surface Area = 21.2(7) + 2(14)

Surface Area = 148.4 + 28

Surface Area = 176.4 cm²

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