#Python 2/3, 252 bytes

import re,math;i=[float(x)if re.match('[\d.]+',x)else x for x in re.sys.stdin.readline().split()]
for o in[0,3if i[0]<'d'else 4]:
 w=i[o+1]*i[o+2]*i[o+3]
 if i[o]<'d':w*=3.14*i[o+1]/i[o+3]
 if i[o]>'s':w*=.5
 a=a/w if o else w
print(math.ceil(a)*i[-1])

Usage Examples:

$ echo 'triangle 10 12.25 3 circle 5 2.2 5' | python stack_codegolf_54454.py
10.0
$ echo 'triangle 5 87.3 20001 rectangle 5.14 2 105.623 0.2' | python stack_codegolf_54454.py
804.2

The Python 2 only and Python 3 only versions are only different in how they receive input; raw_input() for Python 2 and input() for Python 3, as opposed to re.sys.stdin.readline() for the Python2/3 version.

Python 2, 240 bytes

import re,math;i=[float(x)if re.match('[\d.]+',x)else x for x in raw_input().split()]
for o in[0,3if i[0]<'d'else 4]:
 w=i[o+1]*i[o+2]*i[o+3]
 if i[o]<'d':w*=3.14*i[o+1]/i[o+3]
 if i[o]>'s':w*=.5
 a=a/w if o else w
print(math.ceil(a)*i[-1])

Python 3, 236 bytes

import re,math;i=[float(x)if re.match('[\d.]+',x)else x for x in input().split()]
for o in[0,3if i[0]<'d'else 4]:
 w=i[o+1]*i[o+2]*i[o+3]
 if i[o]<'d':w*=3.14*i[o+1]/i[o+3]
 if i[o]>'s':w*=.5
 a=a/w if o else w
print(math.ceil(a)*i[-1])