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) =
=
Distance between (2,5) and (3,2) =
=
Distance between (3,2) and (6,5) =
=
-
Then find base area
Costheta =(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
=
=