Question

The length of the side of a grassy square plot is 80 m. Two walking paths each 4m wide are constructed parallel to the sides of the plot such that they cut each other at the centre of the plot. Determine the area of the paths

Answer 1

According to the problem given :

i ) Length of the side of the grassy square

plot = AB = 80 m

ii ) IJKL and EFGH are two parallel paths

dimensions of the paths are ,

length = l = 80 m

breadth = b = 4 m

iii ) side of the Square PQRS ,

PQ = 4 m

Now ,

Area of the path = 2 × area of IJKL - area of

PQRS

A = 2 × lb - ( PQ )²

= 2 × 80 × 4 - 4²

= 640 - 16

= 624 square metres.

I hope this helps you.

: )

Answer 2

length of the side of grassy square plot = 80m
width of walking path constructed parallel to the sides of the plot such that they cut each other at the centre of the plot = 4m

there are two paths as shown in figure, length of path = 80m and width of path = 4m

for finding total area of paths , we have to subtract area of square PQRS from sum of area of two paths.
as you can see, path is rectangular in shape.
so, area of each path = length × width
= 80m × 4m = 320 m²
so, sum of area of two paths = 2 × 320 = 640m²

now, area of paths = sum of area of two paths - area of square PQRS
= 640 - (4)² = 640 - 16 = 624 m²

hence, area of the paths = 624 m²