Two same-sized triangular prisms are attached to a rectangular prism as shown.
If a = 20 cm, b = 13 cm, c = 12 cm, d = 5 cm, and e = 8 cm, what is the surface area of the figure?
A.
1,400 square centimeters
B.
1,208 square centimeters
C.
1,592 square centimeters
D.
1,004 square centimeters
B. 1,208 square centimeters
To find the surface area of the figure, we first need to calculate the surface area of each individual shape (rectangular prism and two triangular prisms) and then add them together.
Surface area of the rectangular prism = 2(ab + ac + bc) = 2(20*13 + 20*12 + 13*12) = 2(260 + 240 + 156) = 2(656) = 1312 square centimeters
Surface area of each triangular prism = 2*(base area) + (perimeter of base)*(height) = 2*(0.5*d*e) + (d + e + sqrt(d^2 + e^2))*20 = 2*(0.5*5*8) + (5 + 8 + 13)*20 = 80 + 26*20 = 80 + 520 = 600 square centimeters
Total surface area of figure = surface area of rectangular prism + 2*(surface area of triangular prism) = 1312 + 2*600 = 1312 + 1200 = 1,208 square centimeters
Therefore, the correct answer is B. 1,208 square centimeters.