Question

Two cross roads, each of width $10m$, cut at right angles through the centre of a rectangular park of length $700m$ and breadth $300m$ 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.

Answer 1

Finding the area of the park excluding cross roads:

Given:

From the given data we get to know that

Length of the park $\left(L\right)=700m$

Breadth of the park $\left(B\right)=300m$

To find:

We have to determine the area of the roads and the area of the park excluding crossroads in hectares.

Solution:

Step 1: Find the area of the park

$\begin{array}{rcl}Areaofthepark& =& length\times breadth\\ & =& 700\times 300\\ & =& 210000m^2\end{array}$

Step 2: Find area of the cross roads

Let us assume that $ABCD$ is the one cross road and $EFGH$ is another cross road in the park.

The length of $ABCD$ cross road $=700m$

The length of$EFGH$ cross road$=300m$

Since both cross road have the same width $=10m$

Area of the $ABCD$ crossroad

$\begin{array}{rcl}& =& length\times breadth\\ & =& 700\times 10\\ & =& 7000m^2\end{array}$

Area of the $EFGH$ cross road

$\begin{array}{rcl}& =& length\times breadth\\ & =& 300\times 10\\ & =& 3000m^2\end{array}$

Area of the $IJKL$ at center

$\begin{array}{rcl}& =& length\times breadth\\ & =& 10\times 10\\ & =& 100m^2\end{array}$

Area of the roads

$\begin{array}{rcl}& =& \mathrm{Area}\mathrm{of}\mathrm{ABCD}+\mathrm{Area}\mathrm{of}\mathrm{EFGH}–\mathrm{Area}\mathrm{of}\mathrm{IJKL}\\ & =& 7000+3000–100\\ & =& 10000–100\\ & =& 9900{\mathrm{m}}^2\end{array}$

We know that, for $1hectare=10000m^2$

Hence, area of roads in hectares

$$\begin{gathered} =\frac{9900}{10000} \\ =0.99\mathrm{hectare} \end{gathered}$$

Step 3: Find the area of the park excluding cross roads

$\begin{array}{rcl}\mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{park}\mathrm{excluding}\mathrm{roads}& =& \mathrm{Area}\mathrm{of}\mathrm{park}–\mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{roads}\\ & =& 210000–9900\\ & =& 200100{\mathrm{m}}^2\\ & =& \frac{200100}{10000}\\ & =& 20.01\mathrm{hectare}\end{array}$

Therefore Area of roads in hectare$=0.99hectare$ and Area of the park excluding roads$=20.01hectare$