Please answer me question#10 page#97 from following link https://tstuition.wikispaces.com/file/view/3+-+Mensuration.pdf many many thanks

The area of the shaded region can be found out subtracting
the area of the octogon from the area of the circle.

The
area of the octogon could be found adding the areas of the triangles formed within
octogon, joining the center of the circle with each vertex of the octogon. We notice
that the octogon is split into 6 triangles. The central angle within each triangle
measures 360 degrees/6 = 60 degrees. Since the sides that are joining the center of the
circle wich each vertex are equal, being the radius of the circle, then the triangles
inside octogon are equilateral triangles.

We'll calculate
the area of an equilateral triangle:

A = r*r*sin
60/2

A = `r^(2)` `sqrt(3)`
/4

Now, we'll multiply this value by 6, since inside
octogon we have 6 equilateral triangle.

A octogon =
6`r^(2)` `sqrt(3)` /4

A octogon = 3`r^(2)` `sqrt(3)`
/2

All we need now is to calculate the area of the
circle:

A circle = `r^(2)`
`pi`

Now we can determine the area of the shaded
region:

A region = A circle - A
octogon

A region = `r^(2)` (`pi` -
3`sqrt(3)`/2 )