The base of a triangular pyramid is a triangle with corners at (5 ,8 ), (2 ,3 ), and (9 ,4 ). If the pyramid has a height of 4 , what is the pyramid's volume?

1 Answer
Mileena K.
Dec 13, 2017

V=197.63

Explanation:

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So Base values are given. Lets find the length of base:
1) length between (9,4) and (2,3)= sqrt((3-4)^2+(2-9)^2)
= sqrt(50)=5sqrt2=7.07
2)another side length between : (9,4) and (5,8)= sqrt((4-8)^2+(9-5)^2)=4sqrt2=5.65
3) side length between (2,3) and (5,8)= sqrt((2-5)^2+(3-8)^2)=sqrt34=5.83
Volume= V=1/3*Area*h=1/3*4*Area
To find Area, we should use Heron's formula : p=(a+b+c)/2=9.275
area= sqrt[p^3*(p-a)*(p-b)*(p-c)]=148.2257
V=1/3*4*148.2257=197.63

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