Question

which expression can be used to find the surface area of the trapezoidal prism? 6·3 + 6·4 + 6·5 + 6·8 + 23·4 + 1/2(3·4) what is the surface area of the trapezoidal prism? s.a. =? ft² s.a. = 6·3 + 6·4 + 6·5 + 6·8 + 23·4 + 1/2(3·4) = 18 + 24 + 30 + 48 + 34

Explanation:

Step1: Calculate areas of rectangular faces

The trapezoidal - prism has 4 rectangular faces with dimensions:

• Face 1: length = 6 ft, width = 3 ft, area \(A_1=6\times3 = 18\) square - feet
• Face 2: length = 6 ft, width = 4 ft, area \(A_2=6\times4 = 24\) square - feet
• Face 3: length = 6 ft, width = 5 ft, area \(A_3=6\times5 = 30\) square - feet
• Face 4: length = 6 ft, width = 8 ft, area \(A_4=6\times8 = 48\) square - feet

Step2: Calculate areas of trapezoidal bases

The trapezoid has bases \(b_1 = 3\) ft and \(b_2 = 4\) ft and height \(h = 6\) ft. The area of a trapezoid is \(A=\frac{(b_1 + b_2)h}{2}\). For the two trapezoidal bases, the combined area \(A_{bases}=2\times\frac{(3 + 4)\times6}{2}=42\) square - feet

Step3: Calculate total surface area

The surface area \(S.A.\) of the trapezoidal prism is the sum of the areas of the rectangular faces and the trapezoidal bases. \(S.A.=18 + 24+30 + 48+42=162\) square - feet.
The formula for the surface area of the trapezoidal prism is \(S.A.=6\times3+6\times4+6\times5+6\times8 + 2\times\frac{(3 + 4)\times6}{2}\)

Answer:

162