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

Question

1269 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-03T15:18:10

$V = 10/3 units^3$

Let $(A_x, A_y) = (5, 8)$
Let $(B_x, B_y) = (3, 4)$
Let $(C_x, C_y) = (4, 8)$

According to Area of a triangle given 3 points the area, $Delta$ , of the base is:

$Delta = |(A_x(B_y - C_y) + B_x(C_y - A_y) + C_x(A_y - B_y))/2|$

$Delta = |(5(4 - 8) + 3(8 - 8) + 4(8 - 4))/2|$

$Delta = |(5(-4) + 3(0) + 4(4))/2|$

$Delta = |(-20 + 16)/2|$

$Delta = |(-4)/2|$

$Delta = 2$

The volume of the pyramid

$V = 1/3 Deltah$ where h is the height

$V = 1/3 (2)(5)$

$V = 10/3 units^3$

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 5 5 , what is the pyramid's volume?