Mathematics

Grade9

Easy

Question

# Find the area of the regular polygon.

- 250
- 348
- 340
- 289

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: 289

### 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 given figure we can say that,

Length of each side= 6.84

Firstly, we have to find the length of apothem.

For that, consider apothem to be a.

So, tan 70 =

a= tan 70 × 3.42

a= 9.39

Now, we have to find the perimeter of the polygon.

Perimeter= Length of each side of the polygon × No. of sides

= 6.84×9

Area = ×apothem ×Perimeter

= ×9.39 × (9×6.84)

= 289

Thus, the area of the given polygon is 289.

Therefore, the correct option is d, i.e., 289.

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