What is the surface area of the figure? 408ft^2 458ft^2 545ft^2 720ft^2

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

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