A sheet of paper measure 40cm¡Á20cm.A strip 4cm wide is cut from it all around find the area of strip cut out and area of remeining sheet of paper
area of original = 40(20) =800 cm^2
after cutoff, new size is 32 by 12
area of that = 32(12) = 384 cm^2
area of strip cut out = 800-384 = 416 cm^2
To find the area of the strip cut out, we need to find the perimeter of the remaining sheet after the strip has been cut out.
The original sheet of paper measures 40cm by 20cm. When a strip 4cm wide is cut from all around, the length and width of the remaining sheet will be reduced by twice the width of the strip.
So, the dimensions of the remaining sheet will be (40cm - 2 * 4cm) by (20cm - 2 * 4cm), which simplifies to 32cm by 12cm.
To find the perimeter of this new sheet, we can add up all the sides: 32cm + 32cm + 12cm + 12cm = 88cm.
Now, to find the area of the strip cut out, we need to multiply the length of the perimeter (88cm) by the width of the strip (4cm): 88cm * 4cm = 352cm².
Therefore, the area of the strip cut out is 352 square centimeters.
To find the area of the remaining sheet, we can simply multiply the length and width: 32cm * 12cm = 384cm².
So, the area of the remaining sheet of paper is 384 square centimeters.
To find the area of the strip cut out, we need to calculate the perimeter of the remaining sheet of paper after the strip is removed.
1. Calculate the perimeter of the original sheet:
Perimeter = 2 * (Length + Width)
Perimeter = 2 * (40cm + 20cm)
Perimeter = 2 * 60cm
Perimeter = 120cm
2. Deduct the strip width from the perimeter to find the new perimeter:
New Perimeter = Perimeter - 2 * Strip Width
New Perimeter = 120cm - 2 * 4cm
New Perimeter = 120cm - 8cm
New Perimeter = 112cm
3. Calculate the area of the strip cut out:
Area of Strip = Strip Width * New Perimeter
Area of Strip = 4cm * 112cm
Area of Strip = 448cm²
4. Calculate the area of the remaining sheet:
Area of Remaining Sheet = Length * Width - Area of Strip
Area of Remaining Sheet = 40cm * 20cm - 448cm²
Area of Remaining Sheet = 800cm² - 448cm²
Area of Remaining Sheet = 352cm²
Therefore, the area of the strip cut out is 448cm² and the area of the remaining sheet of paper is 352cm².