Question

The figure represents a rectangular lawn with a circular flower bed in the middle.

Find: (i) the area of the whole land

(ii) the area of the flower bed

(iii) the area of the lawn excluding the area of the flower bed

(iv) the circumference of the flower bed.

10m 5m 

Answer 1

Step 1: Find area of the whole land.

Given: The Length of the rectangular lawn $=10m$

The breadth of rectangular lawn$=5m$

The radius of the flower bed$=2m$

Area of the rectangular lawn $=$Length$\times$Breadth

$$\begin{gathered} =10\times 5 \\ =50m^2 \end{gathered}$$

Therefore, the area of the whole land $=50m^2$

Step 2 : Find area of the flower bed

Area of the flower bed $=\mathrm{\pi }\times {\left(\mathrm{radius}\right)}^2$ [Area of circle $={\mathrm{\pi r}}^2$ ]

$$\begin{gathered} =\frac{22}{7}\times {\left(2\right)}^2\left((\because \mathrm{\pi }=\frac{22}{7}\right) \\ =\frac{22}{7}\times 4 \\ =\frac{88}{7} \\ =12.57m^2 \end{gathered}$$

Therefore, the area of the flower bed is $12.57m^2$

Step 3: Find the area of the lawn excluding the area of the flower bed

The area of the lawn excluding the area of the flower bed $=$ Area of rectangular lawn $-$ Area of the flower bed

$$\begin{gathered} =50-12.57 \\ =37.43m^2 \end{gathered}$$

Therefore, the area of the lawn excluding the area of the flower bed is $37.43m^2$

Step 4: Find the circumference of the flower bed

The circumference of the flower bed $=2\times \mathrm{\pi }\times \mathrm{radius}$ [Circumference of circle$=2\mathrm{\pi r}$ ]

$$\begin{gathered} =2\times \frac{22}{7}\times 2\left(\because \mathrm{\pi }=\frac{22}{7}\right) \\ =\frac{88}{7} \\ =12.57\mathrm{m} \end{gathered}$$

Hence, the circumference of the flower bed is $12.57m$