The base of a triangular pyramid is a triangle with corners at $(1 ,1 )$ , $(3 ,6 )$ , and $(4 ,5 )$ . If the pyramid has a height of $5$ , what is the pyramid's volume?

Question

1294 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-12T13:47:38

The volume is $=5.83u^3$

The area of the base is

$A=1/2|(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1)|$

$=1/2(x_1(y_2-y_3)-y_1(x_2-x_3)+(x_2y_3-x_3y_2))$

$A=1/2|(1,1,1),(3,6,1),(4,5,1)|$

$=1/2(1*|(6,1),(5,1)|-1*|(3,1),(4,1)|+1*|(3,6),(4,5)|)$

$=1/2(1(6-5)-1(3-4)+1(15-24))$

$=1/2(1+1-9)$

$=1/2|-7|=7/2$

The volume of the pyramid is

$V=1/3*A*h$

$=1/3*7/2*5$

$=35/6$

$=5.83$

The base of a triangular pyramid is a triangle with corners at (1 ,1 )(1 ,1 ), (3 ,6 )(3 ,6 ), and (4 ,5 )(4 ,5 ). If the pyramid has a height of 5 5 , what is the pyramid's volume?