The base of a triangular pyramid is a triangle with corners at #(6 ,5 )#, #(7 ,1 )#, and #(4 ,7 )#. If the pyramid has a height of #7 #, what is the pyramid's volume?

1 Answer
Aug 17, 2016

Volume of the pyramid is #6.95# cubic unit

Explanation:

The sides of triangular base #A=sqrt((6-7)^2+(5-1)^2)=sqrt17=4.12#;
#B=sqrt((7-4)^2+(1-7)^2)=sqrt45=6.71#;
#C=sqrt((4-6)^2+(7-5)^2)=sqrt8=2.83#; Semi perimeer #s=(4.12+6.71+2.83)/2=6.83#
Area of triangular base#A_t=sqrt(6.83*(6.83-4.12)(6.83-6.71)(6.83-2.83))=2.98#
Volume of the pyramid is #V=(1/3)*A_t*ht = (2.98*7)/3=6.95# cubic unit[Ans}