The base of a triangular pyramid is a triangle with corners at (2,4), (3,2), and (5,5). If the pyramid has a height of 5, what is the pyramid's volume?

1 Answer
May 17, 2018

Volume of triangular base pyramid V=466.47 cub. units

Explanation:

A(2,4),B(3,2),C(5,5)

Using distance formula,

¯¯¯¯¯¯AB=c=(32)2+(24)2=5=2.235

¯¯¯¯¯¯BC=a=(52)2+(54)2=10=3.162

¯¯¯¯¯¯AC=b=(35)2+(25)2=13=3.606

Area of base triangle Ab=s(sa)(sb)(sc)

Semi perimeter sa+b+c2=2.235+3.162+3.6062=18

Ab=1815.76516.83816.394=279.88

Formula for volume of pyramid V=(13)Abh

V=(13)279.885=466.47 cub. units.