The base of a triangular pyramid is a triangle with corners at #(1 ,3 )#, #(2 ,2 )#, and #(8 ,5 )#. If the pyramid has a height of #7 #, what is the pyramid's volume?

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Answer 1 · 2017-09-12T11:12:02

Volume of pyramid is # 10.5 # cu.unit.

#x_1=1 ,y_1=3 ,x_2=2 ,y_2=2,x_3=8 ,y_3=5#

Area of Triangle #A_t= 1/2(x1(y2−y3)+x2(y3−y1)+x3(y1−y2))# or

#A_t= 1/2(1(2−5)+2(5−3)+8(3−2))# or

#A_t= 1/2(-3+4+8)= 9/2 =4.5 # sq.unit

Volume of pyramid is #V_p=1/3*A_b*h ;# where base area

is #A_b = A_t= 4.5 , h=7#( hight).

#:.V_p=1/3*4.5*7 = 10.5 # cu.unit.

Volume of pyramid is # 10.5 # cu.unit. [Ans]