Question

a grassy plot is 80m×60m two cross path each 4m wide are constructed at right angles through the centre of the field,such that each path is parallel to one of the side of the rectangle. find the total area used as path.

Answer 1

Let 1st path ABCD and second path PQRS

Area of path ABCD=80*4=320m2

Area of path PQRS=60*4=240m2

Area of centre square =4*4=16m2

Area of path =320+240-16=544m2

Answer 2

Given:

Length of the grassy plot=80m

Width of the grassy plot=60m

Width of path=4m

To find:

The total area of the path

Solution:

We can find the solution by following a few steps-

We are given that the paths have been constructed at right angles, so the paths intersect each other.

Now we will calculate the area of the path parallel to the length of the field.

Area of path= length of path× width of path

= 80×4

$= {320m}^{2}$

Similarly, the area of the path parallel to the width of the field= width of field×width of path

=60×4

$= {240m}^{2}$

But, the area of the square formed due to the intersection of the paths must be deducted.

So, area of the square= width of the path× width of the path

=4×4

${ = 16m}^{2}$

The total area of the path= area of path parallel to the length + area of path parallel to width- area of the square formed at the intersection.

=320+240-16

${ = 544m}^{2}$

Therefore, the total area of the path is 544m square.