Question

a 1.5 m Footpath runs all along the fence outside in a park 40 metre long and 30 metre wide .what is the perimeter of the fence and what is the area of the footpath

Answer 1

As two dimensions of the park are given, it can be assumed to be a rectangle in shape.

→ perimeter of fence = 40m + 30m + 40m + 30m = 140m

For the area of the path, it runs along all the perimeter of the fence so its length is 140m and its width is 1.5m

→ the area of the footpath next to the fence is 140m x 1.5m = 210 m2.

However, this area only includes the footpath that has one side next to the fence but excludes those parts of the footpath that go round the corners of the fence.

As the path is given as 1.5m wide, it could be assumed that the path at each of the corners will be a quarter circle of radius 1.5m. As there are four of these quarter circles, their total area is the area of a whole circle:

→ area of the path = 210m2 + π x (1.5m)2 = 140m2 + 2.25π m2 ≈ 217.07 m2

The corners could also be squared off, so that each is a square of side 1.5m:

→ area of the path = 210m2 + 4 x (1.5m)2 = 219 m2.

Answer 2

2(l+b)=2(40+30)=140m




Area of the footpath =Total area-Area of the park


=(43*33)-(40*30)

=Area of the footpath