The base of a triangular pyramid is a triangle with corners at #(7 ,5 )#, #(6 ,4 )#, and #(3 ,8 )#. If the pyramid has a height of #4 #, what is the pyramid's volume?

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Answer 1 · 2018-06-06T11:19:40

Volume of a pyramid is #4 2/3# cubic.unit.

Volume of a pyramid is #1/3*#base area #*#hight.

#(x_1,y_1)=(7,5) ,(x_2,y_2)=(6,4),(x_3,y_3)=(3,8) , h=4#

Area of Triangle is

#A_b = |1/2(x_1(y_2−y_3)+x_2(y_3−y_1)+x_3(y_1−y_2))|#

#A_b = |1/2(7(4−8)+6(8−5)+3(5−4))|# or

#A_b = |1/2(-28+18+3)| = | -7/2| =7/2#sq.unit

Volume of a pyramid is

#1/3*A_b*h=1/3 *7/2*4=14/3 = 4 2/3# cubic.unit [Ans]