The base of a triangular pyramid is a triangle with corners at (6 ,3 ), (4 ,7 ), and (8 ,8 ). If the pyramid has a height of 6 , what is the pyramid's volume?

1 Answer
Dec 28, 2017

Volume of pyramid color(red)v= color(purple)(27)

Explanation:

Coordinates of three vertices are
A (6,3), B (4,7), C (8,8)
Height of pyramid h = 6

AB = c = sqrt((4-6)^2 + (7-3)^2) = 4.4721

BC = a = sqrt((8-4)^2 + (8-7)^2) = 4.1231

CA = b = sqrt ((6-8)^2 + (3-8)^2) = 5.3852

Semi perimeter s = (a+b+c)/2 = (4.1231 + 4.4721 + 5.3852) / 2 = 6.9902

Area of base triangle = Delta = sqrt (s (s- a) (s - b) (s - c))

Delta = sqrt (6.9902 * (6.9902-4.1231) * (6.9902-4.4721) * (6.990-5.3852)) = #9

Volume of pyramid v = (1/3) * Delta * h = (1/3) * 9 * 6 = 18