Through a rectangular field of sides 90 m 60 m, two roads are con… - Vidyadip

Question

Through a rectangular field of sides $90\ m \times 60\ m$, two roads are constructed which are parallel to the sides and cut each other at right angles through the centre of the field. if the width of the roads is $3\ m$, find the total area covered by the two roads.

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Answer

Length of the rectangular sheet $=90 m$
Breadth of the rectangular sheet $=60 cm$
Area of the rectangular field $=90 m \times 60 m=5400 m^2$
Area of the road $P Q R S=90 m \times 3 m=270 m^2$
Area of the road $A B C D=60 m \times 3 m=180 m^2$
Clearly, area of KLMN is common to the two roads.
Thus, area of $KLMN =3 m \times 3 m=9 m^2$
Hence, Area of the roads $=$ Area $(P Q R S)+$ Area $(A B C D)-$ Area $(K L M N)$
$=(270+180) m^2-9 m^2=441 m^2$

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