A sheet of paper measures 50 CM by 30cm. A strip 6 CM wide is cut from all around. Find the area of the remaining sheet and also the area of the strip cut out.
area: (50-12)(30-12) = 684
Now subtract that from the 50*30 original area to get the area of the strip.
To find the area of the remaining sheet, we need to subtract the area of the strip cut out from the original area of the sheet.
1. Find the original area of the sheet:
Area = length × width
Area = 50 cm × 30 cm
Area = 1500 cm²
2. Find the area of the strip cut out:
The strip is cut from all around the sheet, so we need to find the combined length of all four sides before calculating the area.
Perimeter = 2(length + width)
Perimeter = 2(50 cm + 30 cm)
Perimeter = 160 cm
Width of the strip = 6 cm
Length of the strip = perimeter of the sheet = 160 cm
Area of the strip = length × width
Area of the strip = 160 cm × 6 cm
Area of the strip = 960 cm²
3. Find the area of the remaining sheet:
Remaining area = Original area - Area of the strip
Remaining area = 1500 cm² - 960 cm²
Remaining area = 540 cm²
Therefore, the area of the remaining sheet is 540 cm², and the area of the strip cut out is 960 cm².
To find the area of the remaining sheet, we need to subtract the area of the strip that is cut out from the original area of the sheet.
Step 1: Calculate the original area of the sheet.
The original area of the sheet is given by the product of its length and width:
Area of the sheet = Length * Width
Given:
Length of the sheet = 50 cm
Width of the sheet = 30 cm
Calculating the area of the sheet:
Area of the sheet = 50 cm * 30 cm = 1500 cm²
Step 2: Calculate the area of the strip that is cut out.
Since a strip of width 6 cm is cut from all around the sheet, the length and width of the remaining sheet will be reduced by 6 cm on each side.
Length of the remaining sheet = Length of original sheet - 2 * Width of the strip
Width of the remaining sheet = Width of original sheet - 2 * Width of the strip
Calculating the length and width of the remaining sheet:
Length of the remaining sheet = 50 cm - 2 * 6 cm
Width of the remaining sheet = 30 cm - 2 * 6 cm
Length of the remaining sheet = 50 cm - 12 cm = 38 cm
Width of the remaining sheet = 30 cm - 12 cm = 18 cm
Step 3: Calculate the area of the remaining sheet.
The area of the remaining sheet is given by the product of its length and width:
Area of the remaining sheet = Length of the remaining sheet * Width of the remaining sheet
Calculating the area of the remaining sheet:
Area of the remaining sheet = 38 cm * 18 cm = 684 cm²
Step 4: Calculate the area of the strip that is cut out.
The area of the strip that is cut out is given by the difference in area between the original sheet and the remaining sheet:
Area of the strip = Area of the sheet - Area of the remaining sheet
Calculating the area of the strip:
Area of the strip = 1500 cm² - 684 cm² = 816 cm²
Therefore, the area of the remaining sheet is 684 cm² and the area of the strip cut out is 816 cm².