Question

The adjoining figure represents a rectangular lawn with a circular flower bed in the middle. \[\]

Find: \[\]
1) The area of the whole land \[\]
2) The area of the flower bed \[\]
3) The area of the lawn excluding the area of the flower bed \[\]
4) The circumference of the flower bed \[\]

Answer 1

Hint: We see that the length $l$ of the rectangular lawn given as $l=10$m , the breadth is given as $b=5$m and the radius of the circular flower bed is $r=2$m, The area of the rectangular lawn is ${{A}_{r}}=l\times b$.T he area ${{A}_{c}}$ and circumference $P$ of circular flower bed are ${{A}_{c}}=\pi {{r}^{2}}$ , $P=2\pi r$. The area of the lawn excluding the area of the flower bed is ${{A}_{r}}-{{A}_{c}}$. \[\]


Complete step by step answer:

We are given in the question a diagrammatic figure of a rectangular lawn which has a circular flower bed in the interior region of the rectangular lawn. \[\]
We know that a rectangle has four sides of two types. The side with more length is called the length of the rectangle and denoted as $l$ and the side with less length compare to $l$ is called the breadth of the rectangle and denoted as $b$. The area is the amount of region a two-dimensional shape occupies in a plane. The area of rectangle ${{A}_{r}}$ is given as
\[{{A}_{r}}=l\times b\]
We also know that in a circle distance from the center to a point on the circle is called radius denoted as $r$. The area ${{A}_{c}}$ of a circle with radius $r$ is
\[{{A}_{c}}=\pi {{r}^{2}}\]
The circumference or perimeter $P$ of a circle is given by
\[P=2\pi r\]
We observe in the figure that the length of the rectangular lawn is given as 10m and the breadth of the rectangular lawn is given as 5m. So we have $l=10$m and $b=5$m. The radius of the circular flower bed is given as 2m. So we have $r=2$m. \[\]
(1) The area of the whole land is the same as the area of the rectangular lawn with length $l=10$m and breadth $b=5$m. So the area of the rectangular lawn is
\[{{A}_{r}}=l\times b=10\text{m}\times 5\text{m}=50{{\text{m}}^{2}}\]
So the area of the whole land is $50{{\text{m}}^{2}}$. \[\]
(2) The area of the flower bed is equal to the area of the circle with radius $r=2$m which is
\[{{A}_{c}}=\pi {{r}^{2}}=3.14\times {{\left( 2\text{m} \right)}^{2}}=12.56{{\text{m}}^{2}}\]
 So the area of the flower bed is $12.56{{\text{m}}^{2}}$. \[\]
(3) The area of the lawn excluding the area of the flower bed is the difference of area between the rectangle and the circle which is
\[{{A}_{r}}-{{A}_{c}}=50-12.56=37.44{{\text{m}}^{2}}\]
 4) The circumference of the flower bed is the circumference of circle with radius s $r=2$m which is\[P=2\pi r=2\times 3.14\times 2=12.56\text{m}\]
So the circumference of the flower bed is 12.56m. \[\]

Note:
We have used the value of $\pi $ here as 3.14. We can also use the value $\pi =\dfrac{22}{7}$ and find the area. We can also find the area of the rectangular lawn with formula$P=2\left( l+b \right)$. We can similarly find the area of a square whose length and breadth are equal with formula $A={{a}^{2}}$ where $a$ is the length of the side.