# 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.

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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 13:36:05