The base of a triangular pyramid is a triangle with corners at $(6 ,4 )$ , $(2 ,1 )$ , and $(3 ,2 )$ . If the pyramid has a height of $4$ , what is the pyramid's volume?

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Answer 1 · 2018-06-09T02:11:56

$color(blue)(V_p = 1/3*A_b*h = 2/3 = 0.667 " cubic.units"$

$"Volume of a pyramid " V_p = 1/3* A_b * h$

$(x_1,y_1)=(6,4) ,(x_2,y_2)=(2,1),(x_3,y_3)=(3,2) , h=4$

Area of Triangle is

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

$A_b = |1/2(6(1−2)+2(2−4)+3(4−1))| = 1/2$

Volume of a pyramid is

$color(blue)(V_p = 1/3*A_b*h=1/3 *1/2*4=2/3 = 0.667 " cubic.units"$

The base of a triangular pyramid is a triangle with corners at (6 ,4 )(6 ,4 ), (2 ,1 )(2 ,1 ), and (3 ,2 )(3 ,2 ). If the pyramid has a height of 4 4 , what is the pyramid's volume?