The base of a triangular pyramid is a triangle with corners at (6 ,2 ), (2 ,7 ), and (3 ,4 ). If the pyramid has a height of 8 , what is the pyramid's volume?

1 Answer
Sep 13, 2017

Volume of pyramid is 9 1/3 cu.unit.

Explanation:

Volume of pyramid V_p= 1/3 * B * h ,where B is base area and

h is hght of pyramid . If (x1, x2), (x2, y2) and (x3, y3) are the

coordinates of vertices of triangle then area of triangle is

A_t= 1/2(x1(y2−y3)+x2(y3−y1)+x3(y1−y2)) or

A_t= 1/2(6(7−4)+2(4−2)+3(2−7)) or

A_t= 1/2(18+4-15) = 3.5

Volume of pyramid V_p= 1/3 * B * h = 1/3 *3.5 *8 =28/3cu.unit

Volume of pyramid is 9 1/3 cu.unit [Ans]