Below is the graph of an irregularly shaped closed region drawn to scale.

Functions that generate the boundary of the region.

Input := 

ftop[x_] = Which[ x <= 4, Sqrt[x] + 10,
    			  4 < x <= 6, 12 - 2 Sin[Pi x],
    			  6 < x <= 8, 21 - x^2/4,
    			  8 < x <= 10, -2.5 x + 25];

Input := 

fbot[x_] = .1 (x - 10)^2;

The Region

Input := 

Plot[{ftop[x], fbot[x]},
	{x, 0, 10},
	PlotRange	-> {0, 15},
	AspectRatio	-> Automatic,
	GridLines	-> 
		{Table[i, {i, 0, 10}],
		 Table[i, {i, 0, 15}]}]

Output =

-Graphics-