Question

Formula to find out the area of a semicircle with radius r is?

Answer 1

Hint: Here, the problem is to find out the formula for the area of a semicircle with radius r. Firstly, we discuss the basic definitions of semicircle and then Formula to find out the area of a semicircle with radius r.

Complete step by step answer:
A semicircle is a half-circle that is formed by cutting a whole circle into two halves along a diameter line. A line segment known as the diameter of a circle cuts the circle into exactly two equal semicircles. The semicircle has only one line of symmetry which is the reflection symmetry. The semicircle is reflection symmetry. The semicircle is also referred to as a half-disk. Since the semicircle is half of the circle (360 degrees), the arc of the semicircle always measures 180 degrees.
Since, we know that the semicircle is half of a circle. You might know that the perimeter of a semicircle is half the perimeter of the circle. But that’s not true.

The perimeter of a semicircle is \[\pi R+2R\], which can also be written as \[R\left( \pi +2 \right)\] by factoring out R.
Where, R= Radius of the semicircle.
\[\pi \]=constant named pi, approximately equal to 3.14
 The unit of the perimeter of a semicircle is cm, metre.
The Area of a half circle generally refers to the space inside the semicircle or the area or region enclosed by it.
Here, the area of a semicircle is half the area of a circle.
The area of a semicircle or the area of a half circle is \[\dfrac{\pi {{R}^{2}}}{2}\].
Where, R= Radius of the semicircle.
\[\pi \]=constant named pi, approximately equal to 3.14
The unit of area of a semicircle is \[{{m}^{2}}\]or \[c{{m}^{2}}\].

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.