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?

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Answer 1 · 2017-09-13T11:19:43

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

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 =28/3#cu.unit

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