A garden is 90 m long and 75 m broad. A path 5 m wide is to be built outside and around it. Find the area of the path. Also find the area of the garden in hectare.
Answers
Answer:
Area of original garden =90×75=6750 m²
After path is added around rectangle, new length =90+2×5=100 m
New breadth =75+2×5=85 m
Area of rectangle with path =100×85=8500 m²
So,
Area of path = Area of rectangle with path − Area of rectangle without path
Area of path =8500−6750
=1750 m²
We know,
1 m ²=0.0001 hectare
So,
6750 m²
=6750×0.0001
=0.675 hectare
Hence area of ground =6750 m²
=0.675 hectares
Therefore, the area of the garden in hectare is 0.675 hectare.
Hint: Here, we will find the area of the path by subtracting the inner area from the outer area of the garden.
Here the garden is in the shape of a rectangle.
Given,
Inner length of the garden (AB) l=90 m
Inner width of the garden (BC) b=75 m
As we know that Area of a rectangle=(Length of the rectangle)×(Width of the rectangle)
So, Area of inner rectangle ABCD=l×b=90×75=6750 m2
According to the problem, a path of 5 m wide is to be built around this garden as shown in figure
Here, Outer length of the garden (PQ) L=l+5+5=90+5+5=100 m
Outer width of the garden (QR) B=b+5+5=75+5+5=85
m
So, Area of the outer rectangle PQRS=L×B=100×85=8500 m2
Area of the path=Area of rectangle PQRS−Area of rectangle ABCD⇒Area of the path=8500−6750=1750m2
Therefore, the area of the path is 1750 m2.
Since, we know that 1 hectare=10000 m2
Also, Area of the garden=Area of inner rectangular ABCD=6750 m2=675010000=0.675 hectare.
Therefore, the area of the garden in hectare is 0.675 hectare.
Note: In the above problem, when a path of 5 m wide is built, the outer dimensions are increased by 10 m in both x and y direction which is clearly visible from the figure.