Okay, here we have this:
Considering the provided figure, we are going to calculate the requested area, so we obtain the following:
So from the given information we have:
Area of the wheel = Area of the inner circle + Area of the ring
And since the area of the inner circle and the ring are equal, we have:
Area of the wheel = Area of the inner circle + Area of the inner circle
Area of the wheel = 2*Area of the inner circle
Remember that the area of a circle is:
Area of the wheel = π r^2
So substituting:
2*Area of the inner circle=π r^2
Area of the inner circle=(π r^2)/2
And the area of each petal of the inner circle is:
Area of each petal’s sector of the inner circle=Area of the inner circle / number of petals
Area of each petal’s sector of the inner circle=((π r^2)/2) / number of petals
Area of each petal’s sector of the inner circle=((π r^2)/2) / 8
So finally replacing with the given information:
Area of each petal’s sector of the inner circle=((π* (6cm)^2)/2) / 8
Area of each petal’s sector of the inner circle=((π* 36cm^2)/2) / 8
Area of each petal’s sector of the inner circle=((36π cm^2)/2) / 8
Area of each petal’s sector of the inner circle=(18π cm^2) / 8
Area of each petal’s sector of the inner circle=18π/8 cm^2
Area of each petal’s sector of the inner circle=2.25π cm^2
Finally we obtain that the Area of each petal’s sector of the inner circle is 2.25π cm^2.
