What is the area of the black section?

You can split this up into 3 parts:

The large triangle with base 16cm and height 24.3cm has an area:
A = 1/2bh
A = 0.5x16x24.3
A = 194.4cm²

One of the other triangles with base 13.5cm and height 12cm has an area:
A = 0.5x12x13.5
A = 81cm²

The last triangle with base 13.5cm and height 5cm has an area:
A = 0.5x13.5x5
A = 33.75cm²

So you have 3 triangle areas. To get the black area, you subtract the two white triangles (in your picture) from the area of the large triangle that was first calculated above so:

Black area = 194.4 - 81 - 33.75 = 79.65cm²
That should be the area... I might have messed up on the basic multiplication, but that's the overall process.