Finding the total area of paths

Question

A rectangular field is of dimension 90×80m. Four paths pass through the field such that two paths each of width 1.5m are parallel to breadth and two paths each of width 2m are parallel to the length. Find the total area of paths.

Answer 1

Two paths occupy $2\cdot 1.5\cdot 80=240\ {\rm m}^2$, and two paths occupy $2\cdot 2\cdot 90=360\ {\rm m}^2$, giving a total of $600\ {\rm m}^2$. Here four rectangles have been counted twice, so that we have to deduct $4\cdot1.5\cdot 2=$ $12\ {\rm m}^2$, which leaves a path area of $588\ {\rm m}^2$.

Answer 2

HINT:

Length $(L)$ of the field without the Path will be $(90-2\cdot1.5)$ M

and the breadth $(B)$ of the same will be $(80-2\cdot2)$ M

So, the area of the field without the Path will be $L\cdot B$

and the area of the field with the Path is $80\cdot 90$ Sq. M