Posted by Sandy on Monday, October 13, 2008 at 5:49pm.
Determine the volume of a triangular prism with sides of the triangular base measuring 10cm, 14 cm, and 21 cm and having height 30 cm.

Math  Damon, Monday, October 13, 2008 at 6:06pm
That will not work because you do not know the altitude of the triangle. You must get the area of the triangular base from the lengths of the three sides.
To find the altitude from the 21 cm base:
call the part next to the 10 cm leg x
call the part next to the 14 cm leg (21x)
call the altitude h
then
x^2 + h^2 = 100
(21x)^2 + h^2 = 196
so
(21x)^2 x^2 =96
441  42x = 96
42 x = 345
x = 8.214
x^2 = 67.47
100x^2 = 32.5 = h^2
h = 5.7
so
(1/2)h *21 = 59.9 = area of base triangle
multiply by 30 to get volume