Question

The diagram shows the outline of a 50 cent from Fiji.
How many lines of symmetry does it have?

(self-made)
A. 12
B. 8
C. 9
D. 6

Answer 1

Hint: A line of symmetry is an imaginary line across which divides the shape exactly into two equal halves. This means that if we fold the shape along the line of symmetry, the two halves will exactly overlap with each other.

Complete step by step answer:
A line of symmetry is an imaginary line across which divides the shape exactly into two equal halves. This means that if we fold the shape along the line of symmetry, the two halves will exactly overlap with each other.
We can also say that a line of symmetry acts like a mirror, where the image of the shape on one side of the line is formed on the other side of the same line. It is exactly the same that a mirror does.
The given shape of the coin is a 12 sided closed-convex polygon. We can also see that all the sides of the polygon are equal in length. Therefore, it is a regular polygon.
Now, if we join the vertices of the polygon that are the exact opposite to each other, we will find that the line exactly divides the shape into two identical halves. Hence, we get one line of symmetry.
Similarly, there are 6 such lines of symmetry in total.
 Now, join the midpoint of any one side to the midpoint of its opposite side. We will get one more line of symmetry. There are 6 such lines of symmetry in total.
Therefore, the total number of lines of symmetry that the coin has is 12.
Hence, the correct option is A.

Note:
A closed-convex polygon is a polygon whose vertices appear to come outwards. The polygon bulges out at the vertices.