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# Through a rectangular field of length $90\ m$ and breadth $60\ m$, two roads are constructed which are parallel to the sides and cut each other at right angles through the centre of the fields. If the width of each road is $3\ m$, find

$(i)$ the area covered by the roads.

$(ii)$ the cost of constructing the roads at the rate of $â‚¹ 110\ per\ m^2$.

Length of the road along the length of the field$= 90\ m$

Breadth$= 3\ m$

Area of the road$= l\times b$

$=90m\times3m=270m^2$

Similarly, the area of the road parallel to the breadth of the field$=l\times b$

$=60\ m\times3\ m=180\ m^2$

Area of the common portion$=3\ m\times3\ m=9m^2$

$(i)$. Area of the two roads

$=270\ m^2+180\ m^2-9\ m^2$

$=450\ m^2-9\ m^2=441\ m^2$

$(ii)$. Cost of constructing the roads

$=Rs\ 110\times441=Rs\ 48,510$

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