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?

1 Answer
sankarankalyanam
Jun 9, 2018

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

Explanation:

#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"#

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