Question

Question

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The total length is 16 inches and width is 10 inches. The length of the removed portion from the bottom right is 12 inches. The shorter portion that is removed has the remaining length of 4 inches. The remaining width after removing the rectangular portion is 6 inches. The shorter portion that is removed has the remaining width of 4 inches.

Nikolai is making an L-shaped platform for his collection of action figures.

What is the surface area of the platform if it is 3 in. thick?

(1 point)
in.2
Remaining Attempts : 3
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Answer 1

To calculate the surface area of the L-shaped platform, we first need to determine the area of the overall rectangle and subtract the area of the removed portion.

1. Calculate the area of the overall rectangle:

   • Length = 16 inches
   • Width = 10 inches
   • Area = Length × Width = 16 in × 10 in = 160 in²

2. Calculate the area of the removed portion:

   • The removed rectangle has dimensions:
     • Width = 4 inches (the shorter dimension remaining)
     • Length = 12 inches (the longer dimension)
   • Area of the removed portion = Length × Width = 12 in × 4 in = 48 in²

3. Calculate the L-shaped area:

   • Area of the L-shaped platform = Area of the overall rectangle - Area of the removed portion
   • Area of the L-shaped platform = 160 in² - 48 in² = 112 in²

4. Calculate the surface area of the platform with thickness:

   • Since the platform is 3 inches thick, the surface area refers to the area of the top surface of the L-shaped platform.
   • The surface area remains 112 in² (as thickness does not change the top surface area).

Therefore, the surface area of the L-shaped platform is 112 in².