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

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Answer 1 · 2018-06-09T02:33:12

$color(maroon)("Volume of a pyramid "V_p = 1/3*A_b*h=18.67 " cubic.units"$

$color(crimson)("Volume of a pyramid " V_p = 1/3* A_b * h$

$(x_1,y_1)=(2,3) ,(x_2,y_2)=(5,1),(x_3,y_3)=(3,5) , h=7$

$color(crimson)("Area of Triangle "$

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

$A_b = |1/2(2(1−5)+5(5−3)+3(3−1))| = 4$

$color(maroon)("Volume of a pyramid "V_p = 1/3*A_b*h=1/3 *8*7=56/3 = 18.67 " cubic.units"$

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