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 baseA_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}