Question

Area of a semicircle is equal to
A) \[\dfrac{1}{2}\] area of the circle
B) \[\dfrac{1}{4}\]area of the circle
C) \[\dfrac{1}{8}\] area of the circle
D) None of these

Answer 1

Hint:
Here we will use the definition of the circle and the concept of the area. We will draw the figure of both circle and semicircle and then compare their areas. The area is the amount of surface covered by a shape in two dimensions.

Complete step by step solution:
Circle is a two dimensional geometric shape which does not have edges and vertices. Now we will draw the figure of a circle.

We know that Area of the circle \[ = \pi {r^2} = \dfrac{\pi }{4}{d^2}\] where, \[r\] is the radius of the circle and \[d\] is the diameter of the circle.
Now we will write the definition of a semicircle.
Semicircle is the shape which is the half of a circle. Now we will draw the figure of a semicircle.

We know that Area of the semicircle \[ = \dfrac{1}{2}\pi {r^2} = \dfrac{\pi }{8}{d^2}\] ,where, \[r\] is the radius of the circle and \[d\] is the diameter of the circle.
Hence we can clearly see from the definition and the figure of the semicircle that the area of the semicircle is equal to half the area of the circle. Therefore, we get
Area of the semicircle \[ = \dfrac{1}{2} \times \]area of the circle

So, option A is the correct option.

Note:
We should know that area is generally measured in square units and is measured for only two dimensional objects. Radius of the circle is half of the diameter of the circle. Circumference of the circle is the outer part of the circle and the total length of the circumference of the circle is known as the perimeter of the circle. We should also know that volume is the amount of space occupied by an object in three-dimensional space. Volume is measured in cubic meters.