The base of a triangular pyramid is a triangle with corners at (6 ,4 ), (2 ,5 ), and (3 ,2 ). If the pyramid has a height of 4 , what is the pyramid's volume?

1 Answer
May 9, 2017

24.47

Explanation:

  • First find the length of each line using formula sqrt ((y_2-y_1)^2 + (x_2-x_1)^2) where 1 and 2 are x and y coordinates of the two points

Distance between (6,4) and (2,5) = sqrt((5-4)^2+(2-6)^2)
= sqrt17
Distance between (2,5) and (3,2) = sqrt((2-5)^2 +(3-2)^2
= sqrt10
Distance between (3,2) and (6,5) = sqrt((5-2)^2 + (6-3)^2)
= 3sqrt2

  • Then find base area
    Cos theta = (b^2+c^2-a^2)/(2*b*c)
    = ((sqrt 17)^2 +(sqrt 10)^2 - (3 sqrt 2)^2)/(2*sqrt10*sqrt17)
    theta = Cos^-1(0.345134245)
    = 69.8^@
    Area = 1/2 *sqrt17 *sqrt10 Sin69.8
    = 6.11822

  • Calculate volume using formula:
    volume = Base area * height

= 6.11822*4
= 24.47