A rectangular nursery bed 10m long and 60m wide is edge on all four sides with a carpet grass step 4m wide. Find the area covered by carpet grass?
just subtract the bed size from the bed+grass area:
(10+8)(60+8) - 10*60 = _____ m^2
extra credit: what would the width of the border have to be to make the grass and the bed have the same area?
To find the area covered by carpet grass, we need to subtract the area of the inner bed from the area of the outer rectangle.
1. Calculate the area of the inner bed:
Area of the inner bed = Length of the bed * Width of the bed
Area of the inner bed = 10m * 60m = 600m²
2. Calculate the area of the outer rectangle:
To calculate the area of the outer rectangle, we need to add the two additional dimensions of the carpet grass to the length and width of the inner bed.
Length of the outer rectangle = Length of the bed + 2 * Width of the carpet grass
Length of the outer rectangle = 10m + 2 * 4m = 10m + 8m = 18m
Width of the outer rectangle = Width of the bed + 2 * Width of the carpet grass
Width of the outer rectangle = 60m + 2 * 4m = 60m + 8m = 68m
Area of the outer rectangle = Length of the outer rectangle * Width of the outer rectangle
Area of the outer rectangle = 18m * 68m = 1224m²
3. Calculate the area covered by carpet grass:
Area covered by carpet grass = Area of the outer rectangle - Area of the inner bed
Area covered by carpet grass = 1224m² - 600m² = 624m²
Therefore, the area covered by the carpet grass is 624 square meters.