Mathematics

Grade9

Easy

Question

# Find the area of the regular polygon.

- 35
- 32
- 21
- 24

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 area of the given polygon.

## The correct answer is: 21

### In the question there is a polygon as shown in the figure above.

Here, we have to find the area of the given polygon.

From the figure we can say that, apothem= 2.5

Firstly, we have to find the length of each side of the polygon.

For that, let us consider length of the polygon be x.

So, tan 64.29 =

x = 1.2

Then, length of each side(a) = 2×1.2 = 2.4

Perimeter(P) = 2.4 × 7 = 16.8

A = ×a ×P

= ×2.5 × 16.8

= 21

So, the area of the given polygon is 21.

Therefore, the correct option is c, i.e., 21.

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