Question
A rectangular park is $45 m$ long and $30 m$ wide. A path $2.5 m$ wide is constructed outside the park. Find the area of the path
✓
Answer
Let $A B C D$ represent the rectangular park and the shaded region between rectangles $A B C D$ and $P Q R S$ represents the path which is $2.5 m$ wide.
To find the area of the path, we need to find $($Area of rectangle $PQRS -$ Area of rectangle $A B C D ).$
Clearly, we have, $\mathrm{PQ}=(45+2.5+2.5) \mathrm{m}=50 \mathrm{~m}$
$P S=(30+2.5+2.5) \mathrm{m}=35 \mathrm{~m}$
Therefore, area of the rectangle $PQRS =l \times b=50 \times 35 \mathrm{~m}^2=1750 \mathrm{~m}^2$
Also, area of the rectangle $A B C D=l \times b=45 \times 30 \mathrm{~m}^2=1350 \mathrm{~m}^2$
Hence, the required s-area of the path $=$ Area of the rectangle $PQRS -$ Area of the rectangle $A B C D$ $=(1750-1350) \mathrm{m}^2=400 \mathrm{~m}^2$
To find the area of the path, we need to find $($Area of rectangle $PQRS -$ Area of rectangle $A B C D ).$
Clearly, we have, $\mathrm{PQ}=(45+2.5+2.5) \mathrm{m}=50 \mathrm{~m}$
$P S=(30+2.5+2.5) \mathrm{m}=35 \mathrm{~m}$
Therefore, area of the rectangle $PQRS =l \times b=50 \times 35 \mathrm{~m}^2=1750 \mathrm{~m}^2$
Also, area of the rectangle $A B C D=l \times b=45 \times 30 \mathrm{~m}^2=1350 \mathrm{~m}^2$
Hence, the required s-area of the path $=$ Area of the rectangle $PQRS -$ Area of the rectangle $A B C D$ $=(1750-1350) \mathrm{m}^2=400 \mathrm{~m}^2$
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