Join B to D. The triangle BAD has twice the dimensions of the shaded triangle so it has 4 times the area=4×8=32cm². But BD is a diagonal of the square, so the area of the square is 2×32=64cm². The square has side length 8, because 8×8=64.
The short legs of the triangles BCM and CDN have length 4cm and long leg 8cm. So together they have an area of 4×8=32cm². Combined with the area of the shaded triangle their total area is 32+8=40cm², so the area of MCN is 64-40=24cm².