A rectangular Park of length 80m and width 65m has two paths of uniform width 2.5m crossing each other. Find the area of remaining portion.
Length of rectangular park = 80 m
Breadth of rectangular park = 65 m
Uniform width of path = 2.5 m
Area of rectangular park = l x b = 80m x 65 m = 5200 sq.m.
Path 1 ( ABCD ) = 80 m
Path 2 ( EFGH ) = 65 m
AB = 2.5 m and AD = 80 m
EH = 2.5 m and EF = 65 m
KLMN which is the square between two cross-roads
KL = 2.5 m and KN = 2.5 m
Area of the path = Area of rectangle ABCD + Area of the rectangle EFGH - Area of the square KLMN
= AD x AB + EF x EH - KL x KN
= (80 x 2.5 + 65 x 2.5 - 2.5 x 2.5) sq.m.
= (200 + 162.5 - 6.25) sq.m.
= 356.25 sq.m.
Area of rectangular park - Area of roads = Area of the remaining portion of park
= 5200 sq.m. - 356.25 sq.m.
= 4,843.75 sq.m. is the area of remaining portion of the park.
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To find the area of the remaining portion of the park, we need to subtract the area of the two paths from the total area of the park.
First, let's calculate the total area of the park:
Area of the park = length × width
Area of the park = 80m × 65m
Area of the park = 5200m²
Next, let's calculate the area of one of the paths:
Area of one path = width of the path × length of the park
Area of one path = 2.5m × 80m
Area of one path = 200m²
Since there are two paths, the total area of the two paths is:
Total area of the paths = 2 × Area of one path
Total area of the paths = 2 × 200m²
Total area of the paths = 400m²
Finally, we can calculate the area of the remaining portion of the park by subtracting the total area of the paths from the total area of the park:
Area of remaining portion = Area of the park - Total area of the paths
Area of remaining portion = 5200m² - 400m²
Area of remaining portion = 4800m²
Therefore, the area of the remaining portion of the park is 4800m².
The area is 80 x 65 = 5200
Path 1 is 2.5 times 80
Path 2 is 2.5 times 65
find these two areas and subtract from the 5200