Mathematics

Grade9

Easy

Question

# The area of a regular hexagon is 54√3 and the perimeter is 36. Find the length of the sides and the apothem.

- s = 6, a =
- s = 8, a =
- s = 8, a =
- s = 6, a =

Hint:

### Polygon is a two- dimensional closed figure which is made up of three or more line segments. Each polygon has its own properties based on the number of sides. Area of a regular polygon can be determined using the formula . Here, we have to find the apothem and length of each side of the given polygon using the area formula.

## The correct answer is: s = 6, a =

### In the question it is given that

Area of a regular hexagon= 54√3

Perimeter of the hexagon= 36

Here, we have to find the length of the sides and the apothem of the given hexagon.

Firstly, find the length of the regular polygon using the perimeter formula.

Perimeter of the polygon= Length of the polygon(s) No. of sides

36= s6

s=

s= 6

Now, find the apothem of the given hexagon using the area formula.

Area of the polygon=

54√3=

a=

a=

So, the length of the regular polygon is 6 and apothem of the given hexagon is .

Therefore, the correct option is a, i.e., s= 6, a= .

A perpendicular line segment joining the centre and one of the sides of the regular polygon is called apothem of the polygon.