question_answer 1)

A verandah of width 2.25 m is constructed all along the outside of a room which is 5.5 m long and 4 m wide. Find: (i) the area of the verandah (ii) the cost of cementing the floor of the verandah at the rate of  ` 200 per \[{{\text{m}}^{\text{2}}}\].

Answer:

                Area of the rectangle \[\text{PQRS}=l\times b\] \[=\text{5}.\text{5 m}\times \text{4 m}=\text{22 }{{\text{m}}^{\text{2}~}}\]                     Area of the rectangle ABCD \[=l\times b\] \[\text{= (5}\text{.5 + 2}\text{.25 + 2}\text{.25) m  }\!\!\times\!\!\text{  (4 + 2}\text{.25 + 2}\text{.25) m}\] \[\text{= 10  }\!\!\times\!\!\text{  8}\text{.50 }{{\text{m}}^{\text{2}}}\text{ = 85 }{{\text{m}}^{\text{2}}}\] (i) Area of the verandah                              = Area of the rectangle ABCD ? Area of the rectangle PQRS            \[\text{= 85 }{{\text{m}}^{\text{2}}}\text{-22 }{{\text{m}}^{\text{2}}}\text{= 63 }{{\text{m}}^{\text{2}}}\] (ii) Cost of cementing the floor of the verandah at the rate of ` 200 per \[{{\text{m}}^{\text{2}}}\] = ` \[63\times 200=\] ` 12,600