Mathematics

Grade9

Easy

Question

# Find the area of the shaded region.

- 56
- 79
- 65
- 84

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 shaded region using the area formula of polygon and circle.

## The correct answer is: 79

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

Here, we have to find the area of the shaded region.

Firstly, we have to find the value of apothem of the given polygon.

So, tan 54 = (where a= apothem)

a= 8.26

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

=12×5 = 60

Area of pentagon =× apothem ×Perimeter

= ×8.26×60 = 247.8

Lastly, find the radius of the given figure.

So, cos 54 =

r = 10.2

Area of Circle = × r × r

= 3.14 ×10.2 ×10.2 = 327

Area of shaded region = area of circle – area of pentagon = 327 – 247.8 = 79.2

Thus, area of the shaded region is approximately equal to 79.

Therefore, the correct option is b, i.e., 79.

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