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Class 7 Perimeter and Area
A nursery school playground is 160 m long and 80 m wide. In it 80 m × 80 m is kept for swings and in the remaining portion, there are 1.5 m wide path parallel to its width and parallel to its remaining length as shown in Figure. The remaining area is covered by grass. Find the area covered by grass.
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To find the area covered by grass in the nursery school playground, we need to calculate the total area of the playground and subtract the areas occupied by the swings and the paths.
Given information:
Length of the playground = 160 m
Width of the playground = 80 m
Area of the swings = 80 m × 80 m
Width of the path = 1.5 m
Step 1: Calculate the total area of the playground.
Total area = Length × Width
Total area = 160 m × 80 m
Total area = 12,800 square meters
Step 2: Calculate the area occupied by the swings.
Area of the swings = 80 m × 80 m
Area of the swings = 6,400 square meters
Step 3: Calculate the area occupied by the paths.
Since there is a 1.5 m wide path parallel to the width and another parallel to the remaining length, we need to calculate the area of both paths and subtract them from the total.
Area of the path parallel to the width:
Length of the path = Length of the playground = 160 m
Width of the path = 1.5 m
Area of the path parallel to the width = Length of the path × Width of the path
Area of the path parallel to the width = 160 m × 1.5 m
Area of the path parallel to the width = 240 square meters
Area of the path parallel to the remaining length:
Length of the path = Width of the playground = 80 m
Width of the path = 1.5 m
Area of the path parallel to the remaining length = Length of the path × Width of the path
Area of the path parallel to the remaining length = 80 m × 1.5 m
Area of the path parallel to the remaining length = 120 square meters
The total area of the paths = Area of the path parallel to the width + Area of the path parallel to the remaining length
Total area of the paths = 240 square meters + 120 square meters
The total area of the paths = 360 square meters
Step 4: Calculate the area covered by grass.
Area covered by grass = Total area – Area of the swings – Total area of the paths
Area covered by grass = 12,800 square meters – 6,400 square meters – 360 square meters
Area covered by grass = 6,040 square meters
Therefore, the area covered by grass in the nursery school playground is 6,040 square meters.
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