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=(25)2+(31)2=9+4=13=3.606

b=(92)2+(43)2=49+1=50=7.071

c=(95)2+(41)2=16+9=25=5

Now for using Heron's formula, s=12(3.606+7.071+5)=15.6772=7.8385

Hence, area of base triangle is

7.8385×(7.83853.606)×(7.83857.071)×(7.83855)

= 7.8385×4.2325×0.7675×2.8385=8.502

Hence, Volume of pyramid is 13×8.502×4=11.336