Answer
$10.66$ square units
Work Step by Step
We know that $K=\frac{a^2\sin(B)\sin(C)}{2\sin(A)}=\frac{b^2\sin(A)\sin(C)}{2\sin(B)}=\frac{c^2\sin(A)\sin(B)}{2\sin(C)}$ and also that the sum of the angles of the triangle is $180^o.$
Hence,
$B=180^o-10^o-100^o=70^o.$
Thus,
$K=\frac{2^2\sin(70^o)\sin(100^o)}{2\sin(10^o)}\approx 10.66.$