Show that the area of the shape can be written as $A=200r-r^2 (2+ \pi/2)$ 
A $\rm200\,m\,$ fence is to placed around a lawn of this shape. 
We know that $x$ in terms of $r$ :
$$x=100-\dfrac{(2+\pi)r}2$$
How do I show that the area of the lawn, $A$, can be written as: 
$$A= 200r-r^2\left(2+\left(\dfracπ2\right)\right)  $$

The area is equal to: $$\eqalign{&x\cdot 2r+\text{half the area of the circle with radius $r$.} \\ &=2r\left[100-\dfrac{(2+\pi)r}2\right]+\dfrac12(\pi r^2).}$$
Then you just have to simplify everything as much as possible and voilà!
