A carpet is laid around a rectangular dance floor measuring 10m by 8m.if the width of the carpet is 2m,find its area.
To find the area of the carpet, we need to consider that the carpet is laid around a rectangular dance floor with dimensions 10m by 8m. The width of the carpet is 2m.
To calculate the area of the carpet, we can find the area of the outer rectangle formed by the carpet and then subtract the area of the inner rectangle formed by the dance floor.
1. Area of the outer rectangle:
To find the area of the outer rectangle, we need to add twice the width of the carpet to both the length and width of the dance floor.
Length of the outer rectangle = Length of the dance floor + twice the width of the carpet
= 10m + 2m + 2m (adding twice the width of the carpet)
= 10m + 4m
= 14m
Width of the outer rectangle = Width of the dance floor + twice the width of the carpet
= 8m + 2m + 2m (adding twice the width of the carpet)
= 8m + 4m
= 12m
Therefore, the area of the outer rectangle is:
Area of the outer rectangle = Length × Width
= 14m × 12m
= 168m²
2. Area of the inner rectangle:
The area of the inner rectangle is simply the area of the dance floor.
Area of the inner rectangle = Length × Width
= 10m × 8m
= 80m²
3. Area of the carpet:
To find the area of the carpet, we subtract the area of the inner rectangle (dance floor) from the area of the outer rectangle (formed by the carpet).
Area of the carpet = Area of the outer rectangle - Area of the inner rectangle
= 168m² - 80m²
= 88m²
Therefore, the area of the carpet is 88 square meters.
To find the area of the carpet, we need to first calculate the dimensions of the carpet.
Given that the width of the carpet is 2 meters, we can determine the length of the carpet by adding twice the width to each dimension of the dance floor.
The length of the carpet = length of the dance floor + 2(width of the carpet)
= 10m + 2(2m)
= 10m + 4m
= 14m
Now that we have the dimensions of the carpet, we can calculate its area by multiplying the length and the width.
Area of the carpet = Length of the carpet × Width of the carpet
= 14m × 2m
= 28m²
Therefore, the area of the carpet is 28 square meters.
Just subtract the bare floor from the total area:
10*8 - (10-2*2)(8-2*2)