For the first part, note that
$Area$(ABD) + $Area$(CBD) = $Area$(ABC)
$Area$(ABD) + 11^2\times \frac{\pi}{18} = \frac12\times 4 \times 11
Which is easy to simplify.
Similarly, for the next part we know
\text{perimeter}(BDC) = |BD| + |DC| + |BC|
You got BD from the first part, and BC...