a) There's no shape name for that, however, it's a hexagonal pyramid put on top of a hexagonal prism's base.
b) There are 3 shape types that make up the surface area; 6 triangles, 6 rectangles and a hexagon. These 13 shapes make the surface area.
Triangles (6)
A = 6(bh/2)
= 6[(6)(5)/2]
= 6(30/2)
= 6(15)
= 90
Rectangles (6)
A = 6(bh)
= 6[(4)(6)]
= 6(24)
= 144
Hexagon (1)
A = [tex] \frac{3 \sqrt{3} }{2} a^2[/tex]
= [tex] \frac{3 \sqrt{3} }{2} 4^2[/tex]
= 5.19/2 (16)
= 2.6 (16)
= 41.6 (ish)
41.6 + 144 + 90
41.6 + 234
275.6
Therefore, surface area is approximately 275.6cm^2
