question_answer 1)

The adjoining figure represents a rectangular lawn with a circular flower bed in the middle. Find. (i) the area of whole land. (ii) the area of flower bed. (iii) the area of the lawn excluding the area of the flower bed. (iv) the circumference of the flower bed.

Answer:

                (i) Area of the whole lawn                 \[=l\times b=\text{10 m  }\!\!\times\!\!\text{  5m = 50 }{{\text{m}}^{\text{2}}}\] (ii) Diameter of the flower bed                          \[=\text{2 m}+\text{2 m}=\text{4 m}\] \[\Rightarrow \] Radius (r) of the flower bed  \[=\text{2 m}\] Area of flower bed \[\text{=  }\!\!\pi\!\!\text{ }{{\text{r}}^{\text{2}}}\text{= }\frac{\text{22}}{\text{7}}\text{ (2}{{\text{)}}^{\text{2}}}\text{ }{{\text{m}}^{\text{2}}}\text{ = }\frac{\text{88}}{\text{7}}{{\text{m}}^{\text{2}}}\text{ =12}\text{.57 }{{\text{m}}^{\text{2}}}\] (iii) Area of the lawn excluding the area of the flower bed = Area of the whole lawn - Area of flower bed \[\text{= 50 }{{\text{m}}^{\text{2}}}\text{-}\frac{\text{88}}{\text{7}}{{\text{m}}^{\text{2}}}\] \[\text{=}\left( \text{50 - }\frac{\text{88}}{\text{7}} \right){{\text{m}}^{\text{2}}}\text{=}\frac{\text{262}}{\text{7}}{{\text{m}}^{\text{2}}}\text{= 37}\text{.43 }{{\text{m}}^{\text{2}}}\] (iv) Circumference of the flower bed    \[=2\pi r\] \[\text{= 2  }\!\!\times\!\!\text{  }\frac{\text{22}}{\text{7}}\text{  }\!\!\times\!\!\text{  2m = }\frac{\text{88}}{\text{7}}{{\text{m}}^{\text{2}}}\text{ = 12}\text{.57}\]