The base of a triangular pyramid is a triangle with corners at (5 ,8 )(5,8), (3 ,4 )(3,4), and (4 ,8 )(4,8). If the pyramid has a height of 6 6, what is the pyramid's volume?

1 Answer

V=4" "V=4 cubic units

Explanation:

To solve for the volume of the pyramid which is
V=1/3*area*heightV=13areaheight

Solve for the area of the triangle first with P_1(3, 4),P_2(5, 8),P_3(4, 8)P1(3,4),P2(5,8),P3(4,8)

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*[(3,5,4,3),(4,8,8,4)]

A=1/2*[3(8)+5(8)+4(4)-5(4)-4(8)-3(8)]

A=1/2*(24+40+16-20-32-24)

A=1/2*(80-76)

A=2

Now the volume V

V=1/3*area*height

V=1/3*2*6=4

V=4" "cubic units

God bless....I hope the explanation is useful.