9514 1404 393
Answer:
(b) 458 ft²
Step-by-step explanation:
The total area is the sum of the L-shaped front and back areas and the areas of the 6 rectangular faces.
The front L-shaped area can be considered to be a 12 ft × 12 ft square with a 5 ft × 7 ft rectangle cut from the upper left corner. Its area is then ...
(12 ft)(12 ft) -(5 ft)(7 ft) = (144 -35) ft² = 109 ft² . . . . front area
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The sum of the areas of the rectangular faces is the product of the width of the figure (5 ft) and the perimeter of the L-shaped face. That perimeter is the sum of the edge lengths. Starting from the lower-left corner and working clockwise, we find the perimeter to be ...
7 ft + 7 ft + 5 ft + 5 ft + 12 ft + 12 ft = 48 ft
Then the sum of rectangular face areas is ...
(48 ft)(5 ft) = 240 ft² . . . . rectangular face area
The total surface area is then ...
2×front area + rectangular face area
= 2×109 ft² +240 ft² = 458 ft² . . . . total surface area
