The base of a triangular pyramid is a triangle with corners at #(3 ,8 )#, #(1 ,6 )#, and #(2 ,8 )#. If the pyramid has a height of #4 #, what is the pyramid's volume?

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Answer 1 · 2018-06-09T19:22:07

#\frac{8}{3}# units^2

The area of the base (triangle) can be worked out from the vertices, as

Area = #{2 * 2}{2} = 2#

Therefore by using the formula

#V = {A * h}{3}# we get the volume as #\frac{2*4}{3} = \frac{8}{3}#

Answer 2 · 2018-06-10T02:52:35

#color(blue)("Volume of a pyramid "V_p = 1/3*A_b*h=1/3 *1*4 = 4/3 #

#"Area of triangle knowing three vertices on the coordinate plane is given by "#

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

#(x_1,y_1)=(3,8) ,(x_2,y_2)=(1,6),(x_3,y_3)=(2,8) , h=4#

#A_b = |1/2(3(6−8)+1(8−8)+2(8−6))| = 1#

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

#color(blue)("Volume of a pyramid "V_p = 1/3*A_b*h=1/3 *1*4 = 4/3 #