a rectangular park is of 90m length and 75m in breadth. A path is made around it with 5width. Area of path??

Area of park + path = 100 x 85 m² = 8500 m ²
______Area of park = 90 x 75 m ² = 6750 m ²
_________________Area of path = 1750 m ²

The creation of the path 5m wide around the perimeter would add 10 m to the total length and 10 m to the total width. (assuming the the edges are squared off). The total area
would be 100m by 85m or 8500 m^2.
Subtracting the park size itself 90m by 75m or 6750m^2 from the total reveals the path size to be 1750m^2.

Alternatively, this could be figured by multiplying 5 meters by the perimeter 330m plus the corners 4 * 5^2 = 1750m^2.

Some people will argue the the corners should be rounded. This would make each corner a quarter circle. Together, all four corners would make a full circle with a radius of 5.
The would make the total area of the corners 25*pi for a total area of approx. 78.54m

so, for squared corners, the area of the path is 1750m^2
and for rounded corners, the area is 1728.54m^2.

Let A= the area of the park
Let P= area of the park
Let A+P = area of the rectangle that includes the path + park

A+P=(90+10)(75+10)=8500
P=(90*75)=6750

A=(A+P)-P = 8500-6750=1750 square meters

I came up with 1650m.
l*w for each segment of the path.
The path's width is 5m.

2(5*75)+2(5*90) = 1650 meters squared

Then you have to take into account that there is an overlap and you'll have to add 10 extra meters to either the length or the width -- your choice (5 on each side) making an extra 100 meters squared.

For a grand total of 1750 meters squared.

Dang. Stupid math.

area of 5m wide path
= [(90 + 10)(75 + 10) -- 90*75 ] m^2
= [8500 -- 6750] m^2
= 1750 m^2

(90 + 5 + 5) x (75 + 5 + 5) - 90 x 75
= 100 x 85 - 90 x 75
= 8500 - 6750
= 1750 m^2

(2(90) + 2(75))*5 = 1650 m^2

area of the park with path is (90 + 10)(75 + 10)
= 100 x 85
= 8500 sqm
area of the park without path is 90 x 75
= 6750 sqm
the difference in the two areas is
= 8500 - 6750
= 1750 sqm