A circular lawn has an area of $154\text{sq. meter}$. A path of $7\text{meter}$ width surrounds the lawn. What is the area of the lawn including the path (in $\text{sq. meter}$)?

Let the inner radius of the circular lawn be $r$.
Given that the area of the circular lawn is $154{\text{m}}^2$:

$$\pi r^2=154$$

$$\frac{22}{7}\times r^2=154$$

$$r^2=154\times \frac{7}{22}$$

$$r^2=7\times 7=49$$

$$r=7\text{m}$$

The path surrounds the lawn with a width of $7\text{m}$. Therefore, the outer radius ($R$) including the path is:

$$R=r+7=7+7=14\text{m}$$

The total area of the lawn including the path is:

$$\text{Area}=\pi R^2=\frac{22}{7}\times 14\times 14$$

$$\text{Area}=22\times 2\times 14=44\times 14=616{\text{m}}^2$$