The shaded figures below are similar.  

1. Solve for $m$ and $n$.

   Hint (a):

   Use the proportion $\frac{22}{10}=\frac{m}{15}$ to find $m$.

   Then write another portion for $n$.

2. Find the area and perimeter of each figure

   Hint (b):

   Can you use the dotted lines to make right triangles so that you can solve for the lengths of the unknown sides?

   Answer (b):

   Perimeter of smaller figure = $80$ cm

   Step 1(b):

   area of rectangle: $(24)(22)=528\text{ cm}^2$

   Step 2(b):

   area of top triangle: $\frac{1}{2}bh=\frac{1}{2}(10)(24)=120\text{  cm}^2$

   Step 3(b):

   area of bottom triangle: $\frac{1}{2}bh=\frac{1}{2}(5)(12)=30\text{  cm}^2$

   More Help (b):

   area of shaded region = rectangle − top triangle − bottom triangle