Explanation:
the area of a triangle is baseline × height / 2.
we have 2 major triangles that define this quadrilateral :
A-D-B and C-D-B.
both triangles have the same baseline : M_D + M_B = 14 cm
what we need to do is get the 2 heights M_C and N_A.
N_A we know already : 8 cm
so,
area A-D-B = 14×8/2 = 14×4 = 56 cm²
M_C we get via Pythagoras of the right-angled triangle D-M-C :
D_C² = M_C² + M_D²
10² = M_C² + 6²
100 = M_C² + 36
64 = M_C²
M_C = 8 cm
so,
area C-D-B = 14×8/2 = 56 cm²
so, the total area of the quadrilateral is
56 + 56 = 112 cm²