The base of a triangular pyramid is a triangle with corners at (6 ,5 ), (2 ,2 ), and (4 ,7 ). If the pyramid has a height of 8 , what is the pyramid's volume?

1 Answer

Volume V=18 2/3=18.67" "cubic units

Explanation:

To solve for the volume of the pyramid which is
V=1/3*area*height

Solve for the area of the triangle first with P_1(2, 2),P_2(6, 5),P_3(4, 7)

the area A matrix

A=1/2*[(x_1,x_2,x_3,x_1),(y_1,y_2,y_3,y_1)]

A=1/2*(x_1*y_2+x_2*y_3+x_3*y_1-x_2*y_1-x_3*y_2-x_1*y_3)

A=1/2*[(2,6,4,2),(2,5,7,2)]

A=1/2*[2(5)+6(7)+4(2)-6(2)-4(5)-2(7)]

A=1/2*(10+42+8-12-20-14)

A=1/2*(60-46)

A=7

Now the volume V

V=1/3*area*height

V=1/3*7*8=56/3

V=18 2/3