To find the length of \( BD \) in the polygon defined by the points \( A(-7,7) \), \( B(-3,6) \), \( D(-3,1) \), and \( C(-7,1) \), we can use the distance formula. The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
For points \( B(-3, 6) \) and \( D(-3, 1) \):
- Use \( B(-3, 6) \) as \( (x_1, y_1) \) and \( D(-3, 1) \) as \( (x_2, y_2) \).
- Substitute the coordinates into the formula:
\[ d = \sqrt{((-3) - (-3))^2 + (1 - 6)^2} \]
This simplifies to:
\[ d = \sqrt{(0)^2 + (-5)^2} \]
\[ d = \sqrt{0 + 25} = \sqrt{25} = 5 \]
Thus, the length of \( BD \) is \( 5 \) cm.
Therefore, the correct response is:
5 cm