The base of a triangular pyramid is a triangle with corners at (8,5), (7,2), and (4,6). If the pyramid has a height of 7, what is the pyramid's volume?

1 Answer
Jul 30, 2018

V=13Abh=(13)7.11717=16.6065, cubic units

Explanation:

Given : A(8,5),B(7,2),C(4,6), h = 7#

Using distance formula we can calculate the lengths of sides a, b, c.

d=(x2x1)2+(y2y1)2

a=(74)2+(26)2=5

b=(48)2+(65)2=17

c=(87)2+(52)2=10

Semi perimeter of base triangle s=a+b+c2

s=5+17+102=12.285426.2427

Area of triangle At=s(sa)(sb)(sc)

At=6.2427(6.24275)(6.242717)(6.242710)

#A_t ~~ 7.1171

Volume of pyramid V=(13)Ath

V=(13)7.11717=16.6065, cubic units