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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