Question

How do you calculate the area of a semicircle with a radius of $ 7\,cm $ ?

Answer 1

Hint: In order to determine the area of the semi-circle, we know that the area of the semicircle is the half the area of the circle. Thus, the area of the circle is $ \pi {r^2} $ . Then, the area of the semi circle is $ \dfrac{{\pi {r^2}}}{2} $ . Here, the radius of the semicircle is given, so by substituting the radius in the formula of the semi-circle, we will determine the area of the semi-circle.

Complete step-by-step answer:
It is give that the radius of the semicircle is $ 7\,cm $ .
We need to determine the area of the semi-circle.
Now, we know that the area of semicircle $ = \dfrac{{\pi {r^2}}}{2} $
Here, from the given $ r = 7\,cm $ and we know that the value of $ \pi $ , i.e., $ \pi = \dfrac{{22}}{7} $ or $ \pi = 3.14 $ .
Now, let us substitute the values in the equation, we have,
Area of the semi-circle $ = \dfrac{{22}}{7} \times {\left( 7 \right)^2} \times \dfrac{1}{2} $
 $ = 11 \times 7 $
 $ = 77\,c{m^2} $
Hence, the area of the semicircle with the radius $ 7\,cm $ is $ 77\,c{m^2} $ .
So, the correct answer is “ $ 77\,c{m^2} $ ”.

Note: It is also important to know about the perimeter of the semi-circle, the perimeter of a semicircle is the sum of the half of the circumference of the circle and diameter. As we know that the perimeter of the circle is $ 2\pi r $ , then the perimeter of the semi-circle is $ \pi r + 2r $ , where $ r $ is the radius.
When the circle is cut into halves or when the circumference of a circle is divided by $ 2 $ , we get a semicircular shape. Since semicircle is half of that of a circle, hence the area will be half that of a circle. The area of the semicircle is the number of square units inside that circle