The part one is because the two said triangles have two angles equal each to each that's why they are similar.
For part two, use their similar properties.
AB /AC = BP /BC
BC = (8*3)/4 = 6
AB /BC = BP /PC
PC = (6*3)/4 = 4.5
You have now the 3 sides of triangle BPC.
Use the Heron's formula for the area.