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Two cross roads, each of width $10\ m$, cut at right angles through the centre of a rectangular park of length $700\ m$ and breadth $300\ m$ and parallel to its sides. Find the area of the roads. Also find the area of the park excluding cross roads. Give the answer in hectares.
From the question, it is given that,
Length of the park $(L) = 700\ m$
Breadth of the park $(B) = 300\ m$
Then,
Area of the park $= length\times breadth$
$= 700\times 300$
$= 210000\ m^2$
Let us assume that $ABCD$ is the one crossroad and $EFGH$ is another crossroad in the park.
The length of $ABCD$ cross road$ = 700\ m$
The length of $EFGH$ cross road $= 300\ m$
Both crossroad have the same width$ = 10\ m$
Then,
Area of the $ABCD$ cross road $= length\times breadth$
$= 700\times 10$
$= 7000\ m^2$
Area of the $EFGH$ cross road$ = length\times breadth$
$= 300\times 10$
$= 3000\ m^2$
Area of the $IJKL$ at center$ = length\times breadth$
$= 10\times 10$
$= 100\ m^2$
Area of the roads $=$ Area of $ABCD +$ Area of $EFGH-$ Area of $IJKL$
$= 7000 + 3000 – 100$
$= 10000 – 100$
$= 9900\ m^2$
We know that for $1\ hectare = 10000\ m^2$
Hence, area of roads in hectare $= \frac{9900}{10000}$
$= 0.99\ hectare$
Finally, Area of the park excluding roads $=$ Area of park $-$ Area of the roads
$= 210000-9900$
$= 200100\ m^2$
$= \frac{200100}{10000}$
$= 20.01\ Hectare$
Updated on: 10-Oct-2022
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