Question

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.

Answer 1

Here, PQ$$=10$$m and PS$$=300$$m, EH$$=10$$m and EF$$=700$$m

And KL$$=10$$m and KN$$=10$$m

Area of roads $$=$$ Area of PQRS$$ + $$Area of EFGH$$ - $$Area of KLMN

$$[\because$$ KLMN is taken twice, which is to be subtracted$$]$$

$$=PS\times PQ+EF\times EH-KL\times KN$$

$$=(300\times 10)+(700\times 10)-(10\times 10)$$

$$=3000+7000-100$$

$$=9,900m^2$$

Area of road in hectares, $$1m^2=\dfrac{1}{10000}$$hectares

$$\therefore 9,900m^2=\dfrac{9900}{10000}=0.99$$ hectares

Now, Area of park excluding cross roads $$=$$ Area of park$$-$$Area of road

$$=(AB\times AD)-9,900$$

$$=(700\times 300)-9,900$$

$$=2,10,000-9,900$$

$$=2,00,100\ m^2\\$$

$$=\dfrac{200100}{10000}$$ hectares$$=20.01$$ hectares.