The base of a triangular pyramid is a triangle with corners at (3,8), (1,6), and (2,8). If the pyramid has a height of 4, what is the pyramid's volume?

2 Answers
Jun 9, 2018

83 units^2

Explanation:

The area of the base (triangle) can be worked out from the vertices, as

Area = {22}{2}=2

Therefore by using the formula

V={Ah}{3} we get the volume as 243=83

Jun 10, 2018

Volume of a pyramid Vp=13Abh=1314=43

Explanation:

https://www.onlinemathlearning.com/area-triangle.html

Area of triangle knowing three vertices on the coordinate plane is given by

Ab=12(x1(y2y3)+x2(y3y1)+x3(y1y2))

(x1,y1)=(3,8),(x2,y2)=(1,6),(x3,y3)=(2,8),h=4

Ab=12(3(68)+1(88)+2(86))=1

Volume of a pyramid Vp=13Abh

Volume of a pyramid Vp=13Abh=1314=43