inside a rectangular field there is a path 2 meter wide on all sides.If the dimension of the fields are 40 meter and 25meter. Find the area of the field
A = ( 40 - 2 * 2 ) * ( 25 - 2 * 2 ) = ( ( 40 - 4 ) * ( 25 - 4 ) = 36 * 21 = 756 m ^ 2
Remark:
Length and width have path 2 meter wide for both sides.
That's why we need to reduce their sizes by 2 m * 2 m
Area of rectangle :
A = a * b
where
a = L - 2 * 2 = 40 - 2 * 2 = 40 - 4 = 36 m
b = W - 2 * 2 = 25 - 2 * 2 = 25 -4 = 21 m
So :
A = a * b = 36 * 21 = 756 m ^ 2
To find the area of the field, we need to subtract the area of the inner rectangular path from the area of the outer rectangle.
First, let's calculate the area of the outer rectangle. The dimensions are given as 40 meters by 25 meters. So, the area of the outer rectangle is:
Area_outer = length × width
= 40 × 25
= 1000 square meters
Next, let's calculate the dimensions of the inner rectangular path. Since there is a 2-meter wide path on all sides, we need to subtract 2 meters from each dimension of the outer rectangle to get the dimensions of the inner rectangle.
Length_inner = length_outer - 2 × 2 (2 meters on each side)
= 40 - 4
= 36 meters
Width_inner = width_outer - 2 × 2 (2 meters on each side)
= 25 - 4
= 21 meters
Now, let's calculate the area of the inner rectangle. The dimensions are 36 meters by 21 meters.
Area_inner = length_inner × width_inner
= 36 × 21
= 756 square meters
Finally, to find the area of the field, we subtract the area of the inner rectangle from the area of the outer rectangle:
Area_field = Area_outer - Area_inner
= 1000 - 756
= 244 square meters
Therefore, the area of the field is 244 square meters.