find the area of the polygon.\nthe area of the polygon is \n(type a whole number.)

Explanation:

Step 1: Decompose the polygon into a central rectangle and four triangles

The polygon can be divided into a central rectangle with dimensions (8 , \text{cm} \times 8 , \text{cm}), two top/bottom triangles with base (8 , \text{cm}) and height (4 , \text{cm}), and two side triangles with base (7 , \text{cm}) and height (4 , \text{cm}).

Step 2: Calculate the area of the central rectangle

[ \text{Area}_{\text{rectangle}} = 8 \times 8 = 64 , \text{cm}^2 ]

Step 3: Calculate the total area of the top and bottom triangles

Each top/bottom triangle has area (\frac{1}{2} \times 8 \times 4 = 16 , \text{cm}^2), so two triangles: [ 2 \times 16 = 32 , \text{cm}^2 ]

Step 4: Calculate the total area of the side triangles

Each side triangle has area (\frac{1}{2} \times 7 \times 4 = 14 , \text{cm}^2), so two triangles: [ 2 \times 14 = 28 , \text{cm}^2 ]

Step 5: Sum all areas

[ \text{Total Area} = 64 + 32 + 28 = 124 , \text{cm}^2 ]

Answer:

124