Answer:
Part a: The parametric equations of the curve are as indicated

Part b: The area under the curve is

Explanation:
Part a
As the wheel rolls the path traced by the point is a cycloid which is as given as
As the radius is 1 the equation is

The parametric equations of the curve are as indicated above.
Part b
The area under the curve is given as

Here
y is given as

and x is given as
Finding its differential as
![{dx}=[(1)/(2)-cos \theta]}d\theta](https://img.qammunity.org/2021/formulas/mathematics/college/a8gbqh4uawk1ykluq6ji7nesr1zft6ygln.png)
Substituting in the equation and solving the equation
![\int_(0)^(2 \pi) ydx\\\int_(0)^(2 \pi) [(1)/(2)+(1)/(2)(1-cos \theta)][(1)/(2)-cos \theta]}d\theta]\\\int_(0)^(2 \pi) [((cos(\theta)-2)(2cos(\theta)-1))/(4)d\theta]\\=(9 \pi)/(4)](https://img.qammunity.org/2021/formulas/mathematics/college/exlvaa8k1jdgi3mqf99pcvlqophrsd2cz4.png)
So the area under the curve is
