Two roads of width 5 m run perpendicular to each other in the middle of a
rectangular garden. The garden is of length 80m and width 60m. Find the
area of the road and hence the area of the remaining portion of the garden.
Answers
Given:
✰ Two roads of width 5 m run perpendicular to each other in the middle of a rectangular garden.
✰ Length of garden = 80 m
✰ Breadth of garden = 60 m
To find:
✠ Area of the road.
✠ Area of the remaining portion of the garden.
Solution:
✭ Area = length × breadth ✭
➛ Width of the roads = 5 m
➛ Length of first perpendicular road = Length of rectangular garden
➛ Length of first perpendicular road = 80
➛ Area of first perpendicular road = 80 × 5
➛ Area of first perpendicular road = 400 m²
➛ Length of second perpendicular road = Breadth of rectangular garden
➛ Length of second perpendicular road = 60
➛ Area of second perpendicular road = 60 × 5
➛ Area of second perpendicular road = 300 m²
➛ Area of common portion of road that lies at the centre of the park = 5 × 5
➛ Area of common portion of road that lies at the centre of the park = 25 m²
Now, we will add both the area of first and second road but we will substract area of common portion because it is repeated twice.
➤ Area of the road = Area of first road + Area of second road - Area of common portion of road
➤ Area of the road = ( 400 + 300 ) - 25
➤ Area of the road = 700 - 25
➤ Area of the road = 675 cm²
∴ The area of the road = 675 cm²
Now, find out the area of the remaining portion of the garden. To find it, we will substract area of road from the area of garden. First find out the area of garden.
➛ Area of rectangular garden = 80 × 60
➛ Area of rectangular garden = 4800 cm²
➤ Area of the remaining portion of the garden = Area of rectangular garden - Area of the road
➤ Area of the remaining portion of the garden = 4800 - 675
➤ Area of the remaining portion of the garden = 4125 m²
∴ Area of the remaining portion of the garden = 4125 m²
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