A rectangular carpet was placed in a rectangular floor which is 8m long and 7m wide leaving 1m border all around it. Find the area of the carpet. Find the area of the uncovered part of the floor.?
To find the area of the carpet, we need to subtract the area of the border from the area of the floor.
Step 1: Calculate the area of the floor
Since the floor is rectangular, we can calculate its area by multiplying the length by the width.
Area of the floor = Length × Width
Area of the floor = 8m × 7m
Area of the floor = 56m²
Step 2: Calculate the area of the border
The border is 1m wide all around the carpet. To calculate the area of the border, we need to subtract the area of the inner rectangle from the area of the outer rectangle.
Area of the border = (Length of outer rectangle × Width of outer rectangle) - (Length of inner rectangle × Width of inner rectangle)
Length of outer rectangle = (Length of carpet + 2 × width of border)
Length of outer rectangle = (8m + 2m)
Length of outer rectangle = 10m
Width of outer rectangle = (Width of carpet + 2 × width of border)
Width of outer rectangle = (7m + 2m)
Width of outer rectangle = 9m
Length of inner rectangle = Length of carpet
Length of inner rectangle = 8m
Width of inner rectangle = Width of carpet
Width of inner rectangle = 7m
Area of the border = (10m × 9m) - (8m × 7m)
Area of the border = 90m² - 56m²
Area of the border = 34m²
Step 3: Calculate the area of the carpet
Area of the carpet = Area of the floor - Area of the border
Area of the carpet = 56m² - 34m²
Area of the carpet = 22m²
Step 4: Calculate the area of the uncovered part of the floor
The uncovered part of the floor is the area of the border.
Area of the uncovered part of the floor = Area of the border
Area of the uncovered part of the floor = 34m²
Therefore, the area of the carpet is 22m², and the area of the uncovered part of the floor is 34m².
To find the area of the carpet, you need to subtract the area of the border from the total area of the floor.
The total area of the floor can be found by multiplying its length and width:
Area of the floor = Length × Width
= 8m × 7m
= 56m²
The area of the border can be calculated by subtracting the inner rectangle (carpet) from the outer rectangle (floor).
The outer rectangle has dimensions 8m by 7m, and the inner rectangle has dimensions (8m - 2m) by (7m - 2m) to account for the 1m border on all sides.
Area of the border = (8m × 7m) - (6m × 5m)
= 56m² - 30m²
= 26m²
Finally, the area of the carpet is obtained by subtracting the area of the border from the total area of the floor:
Area of the carpet = Area of the floor - Area of the border
= 56m² - 26m²
= 30m²
Therefore, the area of the carpet is 30m².
To find the area of the uncovered part of the floor, you subtract the area of the carpet from the total area of the floor:
Area of the uncovered part of the floor = Area of the floor - Area of the carpet
= 56m² - 30m²
= 26m²
Therefore, the area of the uncovered part of the floor is 26m².
each of the carpet's dimensions is 2 m less than the floor dimensions
... one m on each end and each side
so the carpet is 6 m long and 5 m wide ... area = 6 m * 5 m = ? m^2
the area of the floor is ... 8 m * 7 m = ? m^2