Question

Question 6

Two crossroads, each of width 10 m, cut at right angle through the center 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 crossroads. 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 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, $1m^2=\frac{1}{10000}hectares$
$\therefore$ $9,900m^2=\frac{9900}{10000}=0.99hectares$
Now, Area of park excluding cross roads
= Area of park - Area of roads
$=(AB\times AD)-9,900$
$=(700\times 300)-9,900$
$=2,10,000-9,900$
$=200100m^2$
$=\frac{200100}{1000}hectares=20.01hectares$