What is the surface area of the figure? A. 408 ft2 B. 458 ft2 C. 545 ft2 D. 720 ft2

There are 2 faces 7 x 5

\( 2*(5*7)=2*35=70ft^2 \)

There 2 faces 5 x 5

\( 2*(5*5)=2*25=50ft^2 \)

there are 3 faces 5 x 12

\( 4*(5*12)=4*60=240ft^2 \)

There are 2 faces 7 x 7

\( 2*(7*7)=2*49=98ft^2 \)

Now only we have to sum all of them together

\( 98+240+50+70=458ft^2 \)

\( cuboid : \\ \\ l=12 \ ft, \ \ w = 5 \ ft, \ \ h= 7 \ ft \\ \\ A = 2wl + 2lh + 2hw \\ \\A=2\cdot 5\cdot 12 + 2\cdot 12\cdot 7 + 2\cdot 7\cdot 5 = 120+ 168 +70 = 358 \ ft^2 \\ \\ cube: \\ \\ four \ side \ walls : \\ \\ s= 5 \ ft \\ \\ 4 \cdot s^2 = 4 \cdot 5^ 2 = 4*25 = 100 \ ft^2 \\ \\ surface \ area \ of \ the \ figure : \\ \\ 358 +100 = 458 \ ft^2 \\ \\ Answer : \ B. \ 458 ft^ 22 \)


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