In the figure, the area of the shaded region is 224π cm^2.

what is the value of x?

(my answer is 7)

Here is my take... I'm getting x = 10 as an answer.  Here was my approach.  

Overall: the area of the large circle minus the area of the small circle will give the area of the shaded region.. the following is how this looks mathematically:

Recall: Area of a circle is defined by πr² and I will be using 'x' as the radius of the smaller circle.  So:
324π is the area of the large circle and (x)²(π) represents the area of the smaller circle:  

Now 324π - x²(π) = 224π
or,  324 - x² = 224
or x² = 100
and now you can see x = 10

Total area is 50 sqr ft

Step-by-step explanation:

The area can be found by splitting the shape into a rectangle and a triangle

The area of rectangle is l x w which would become 8 x 3 = 24 ft

Similarly the area of triangular shape would be 1/2 (lxw)

So area of triangular shape would be 1/2 (4 x 4) = 8

Since there are two triangles so area would be 8 + 8 =16

Now total area will be 16 + 24

Area = 50 sqr ft