Use the image to answer the question.
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?
please subtract connecting sides
To find the surface area of the L-shaped platform, we first need to find the area of each individual rectangle and then subtract the overlapping area.
The total area of the platform before any portions are removed is:
Total Area = Length x Width = 16in x 10in = 160in²
Next, we need to find the area of the portion that was removed from the bottom right:
Area of removed portion = 12in x 4in = 48in²
Now, we need to subtract the overlapping area since the removed portion is L-shaped:
Area of overlapping portion = (12in - 4in) x 4in = 8in x 4in = 32in²
Therefore, the total area of the removed portion is 48in² - 32in² = 16in²
Now, we can find the area of the remaining platform:
Remaining Area = Total Area - Removed Area = 160in² - 16in² = 144in²
Finally, to find the total surface area of the L-shaped platform with a thickness of 3 in., we multiply the remaining area by the thickness:
Surface Area = Remaining Area x Thickness = 144in² x 3in = 432in²
Therefore, the surface area of Nikolai's L-shaped platform is 432 square inches.
nope
I apologize for the mistake in my previous response. Let's try again to find the correct surface area of the L-shaped platform.
The total length of the platform is 16 inches, and the total width is 10 inches.
The length of the removed portion is 12 inches, and the remaining length is 4 inches.
The width of the removed portion is 4 inches, and the remaining width is 6 inches.
The thickness of the platform is 3 inches.
To find the surface area of the L-shaped platform with a thickness of 3 inches, we need to find the individual areas of each rectangular section and then subtract the overlapping area.
The total area of the platform before any portions are removed is:
Total Area = Length x Width = 16in x 10in = 160in²
The area of the removed portion is:
Area of removed portion = 12in x 4in = 48in²
We must subtract the overlapping area due to the L-shape:
Area of overlapping portion = 4in x 4in = 16in²
Therefore, the total area of the removed portion, considering the overlapping area, is 48in² - 16in² = 32in²
Now, we can find the remaining area of the platform:
Remaining Area = Total Area - Removed Area = 160in² - 32in² = 128in²
Finally, to find the total surface area of the L-shaped platform with a thickness of 3 in., we multiply the remaining area by the thickness:
Surface Area = Remaining Area x Thickness = 128in² x 3in = 384in²
Therefore, the correct surface area of Nikolai's L-shaped platform with a thickness of 3 inches is 384 square inches.
not that either
I apologize for the errors in my previous responses. Let's correct it and find the correct surface area of the L-shaped platform with a thickness of 3 inches.
Given information:
Total length of the platform = 16 inches
Total width of the platform = 10 inches
Removed portion length = 12 inches
Removed portion width = 4 inches
Remaining width after removing the portion = 6 inches
Thickness of the platform = 3 inches
First, we need to find the area of the platform before any portions are removed:
Total Area = Length x Width = 16in x 10in = 160in²
Next, let's find the area of the removed portion:
Area of removed portion = 12in x 4in = 48in²
Now, we subtract the overlapping area due to the L-shape:
Area of overlapping portion = (12in - 4in) x 4in = 8in x 4in = 32in²
Therefore, the total area of the removed portion, considering the overlapping area, is 48in² - 32in² = 16in²
Now, we can find the remaining area of the platform:
Remaining Area = Total Area - Removed Area = 160in² - 16in² = 144in²
Since the platform has a thickness of 3 inches, we multiply the remaining area by the thickness to find the surface area:
Surface Area = Remaining Area x Thickness = 144in² x 3in = 432in²
Therefore, the correct surface area of Nikolai's L-shaped platform with a thickness of 3 inches is 432 square inches. Thank you for your patience.
really
I apologize for the errors in my previous responses. Let's recalculate the surface area of the L-shaped platform with the correct information provided in the image.
Given information:
Total length of the platform = 16 inches
Total width of the platform = 10 inches
Thickness of the platform = 3 inches
Length of the removed portion from the bottom right = 12 inches
Remaining length after removing the portion = 4 inches
Width of the removed portion = 4 inches
Remaining width after removing the portion = 6 inches
To find the surface area of the L-shaped platform, we first calculate the area of the full platform:
Total Area = Total length x Total width
Total Area = 16 inches x 10 inches
Total Area = 160 square inches
Next, we calculate the area removed from the platform:
Area of the removed portion = Length of removed portion x Width of removed portion
Area of the removed portion = 12 inches x 4 inches
Area of the removed portion = 48 square inches
Now, we subtract the area of the removed portion to find the remaining area:
Remaining Area = Total Area - Area of the removed portion
Remaining Area = 160 square inches - 48 square inches
Remaining Area = 112 square inches
Finally, to find the surface area of the L-shaped platform with a thickness of 3 inches, we multiply the remaining area by the thickness:
Surface Area = Remaining Area x Thickness
Surface Area = 112 square inches x 3 inches
Surface Area = 336 square inches
Therefore, the surface area of Nikolai's L-shaped platform with a thickness of 3 inches is 336 square inches. Thank you for your understanding.
3 inches thick= 3 inches wide
Let's recalculate the surface area of the L-shaped platform considering the thickness of 3 inches as part of the width.
Given information:
Total length of the platform = 16 inches
Total width of the platform = 10 inches (including the 3-inch thickness)
Thickness of the platform = 3 inches
Length of the removed portion from the bottom right = 12 inches
Remaining length after removing the portion = 4 inches
Width of the removed portion = 4 inches
Remaining width after removing the portion = 6 inches (including the 3-inch thickness)
To find the surface area of the L-shaped platform, we first calculate the complete area of the platform including the thickness:
Total Area = Total length x Total width (including thickness)
Total Area = 16 inches x 10 inches = 160 square inches
Next, we calculate the area removed from the platform:
Area of the removed portion = Length of removed portion x Width of removed portion
Area of the removed portion = 12 inches x 4 inches = 48 square inches
Now, we subtract the area of the removed portion to find the remaining area:
Remaining Area = Total Area - Area of the removed portion
Remaining Area = 160 square inches - 48 square inches = 112 square inches
To find the surface area including the thickness of 3 inches, we consider the width including the 3-inch thickness:
Width of platform with thickness = 10 inches (original width) + 3 inches (thickness) = 13 inches
Finally, we calculate the corrected surface area of the L-shaped platform with the thickness included:
Surface Area = Remaining Area x Width (including thickness)
Surface Area = 112 square inches x 13 inches = 1456 square inches
Therefore, the surface area of Nikolai's L-shaped platform, including the 3-inch thickness as part of the width, is 1456 square inches. Thank you for your patience and clarification.