question_answer

A rectangular lawn is 50 m long and 30 m wide. It has roads 2 m wide goiling the middle points of the opposite side and also a path of same breadth running inside it. The total area of all the paths and roads is

A) \[1050\,\,{{m}^{2}}\]              

B) \[928\,\,{{m}^{2}}\]

C) \[444\,\,{{m}^{2}}\]    

D) \[428\,\,{{m}^{2}}\]

Correct Answer: C

Solution :

Area of ABCD \[=50\times 30=1500\,\,{{m}^{2}}\]

Area of EFGH \[=46\times 26=1196\,\,{{m}^{2}}\]

Area of path \[=1500-1196=304\,\,{{m}^{2}}\]

Area of shaded square \[=2\times 2=4\,\,{{m}^{2}}\]

Area of roads \[=26\times 2+46\times 2=144\,\,{{m}^{2}}\]

Area of road \[=144-4=140\,\,{{m}^{2}}\]

Area of road and path \[=304+140=444\,\,{{m}^{2}}\]