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]

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