The base of a triangular pyramid is a triangle with corners at (5 ,1 ), (2 ,3 ), and (9 ,4 ). If the pyramid has a height of 4 , what is the pyramid's volume?

1 Answer
Mar 18, 2016

Volume of pyramid is 11.336 units

Explanation:

First to find area of base, let us find all the sides of base triangle.

a=sqrt((2-5)^2+(3-1)^2)=sqrt(9+4)=sqrt13=3.606

b=sqrt((9-2)^2+(4-3)^2)=sqrt(49+1)=sqrt50=7.071

c=sqrt((9-5)^2+(4-1)^2)=sqrt(16+9)=sqrt25=5

Now for using Heron's formula, s=1/2(3.606+7.071+5)=15.677/2=7.8385

Hence, area of base triangle is

sqrt(7.8385xx(7.8385-3.606)xx(7.8385-7.071)xx(7.8385-5)

= sqrt(7.8385xx4.2325xx0.7675xx2.8385)=8.502

Hence, Volume of pyramid is 1/3xx8.502xx4=11.336