Question

Find the area of the semi-circle whose radius is 7 cm.

Answer 1

Hint: For solving this question first we will see some important formulas related to the circle like the area of the circle is given by $\pi {{r}^{2}}$ where $r$ is the radius of the circle. After that, we will calculate the area of the circle of radius 7 cm and then the area of the semi-circle will be half of the value of the area of the circle.
Complete step-by-step answer:
Given: It is given that there is a semicircle of radius 7 cm and we have to find the value of its area.
Now, before we proceed we should know the following two formulas:
1. For a circle of radius $r$ units, then the value of circumference is equal to $2\pi r$ units.
2. For a circle of radius $r$ units, then the value of the area of the circle is equal to $\pi {{r}^{2}}$ sq. units.
Here, we will be using the formula mentioned above in the second point.
Now, let there be a circle of 7 cm. So, the value of the area of the circle can be calculated from the formula $\pi {{r}^{2}}$ where $r=7$ cm. Then,
$\begin{align}
  & Are{{a}_{Circle}}=\pi {{r}^{2}} \\
 & \Rightarrow {\text{Area}_{\text{Circle}}}=\pi \times {{7}^{2}} \\
 & \Rightarrow {\text{Area}_{\text{Circle}}}=49\pi \text{ c}{{\text{m}}^{2}} \\
\end{align}$
Now, the semicircle will be one half of the circle. For more clarity look at the figure given below:

In the above figure, we have a semi-circle whose centre is at point A and its radius is 7 cm.
Now, as we know that the semi-circle will be one half of the circle. So, the area of the semi-circle will be half of the value of the area of the circle. Then,
$\begin{align}
  & Are{{a}_{Semi-circle}}=\dfrac{Are{{a}_{circle}}}{2} \\
 & \Rightarrow {\text{Area}_{\text{Semi-circle}}}=\dfrac{49\pi }{2}=\dfrac{49}{2}\times \dfrac{22}{7} \\
 & \Rightarrow {\text{Area}_{\text{Semi-circle}}}\approx 77\text{ c}{{\text{m}}^{2}} \\
\end{align}$
Now, from the above result, we conclude that the area of the given semi-circle will be $77\text{ c}{{\text{m}}^{2}}$.

Note: Here, the student should know about the geometry of the circle and we should try to understand it with the help of practical examples like the shape of the circular plate, bottle cap etc. Moreover, though the question is very easy, we should know the concept of the semi-circle and how we get its area from the area of the full circle.