The base of a triangular pyramid is a triangle with corners at #(6 ,2 )#, #(3 ,5 )#, and #(4 ,2 )#. If the pyramid has a height of #8 #, what is the pyramid's volume?

Question

The base of a triangular pyramid is a triangle with corners at #(6  ,2  )#, #(3  ,5   )#, and #(4  ,2  )#.  If the pyramid has a height of #8  #, what is the pyramid's volume?

Autumn Armstrong · Accepted Answer

#V=8" "#cubic units

the volume #V# of a triangular pyramid has the formula Volume is equal to 1/3 of base area * pyramid height. Let us compute the area #A# of the base with #P_1(x_1, y_1)=(6, 2)# #P_2(x_2, y_2)=(3, 5)# #P_3(x_3, y_3)=(4, 2)# #A=1/2[(x_1, x_2, x_3, x_1),(y_1, y_2, y_3, y_1)]# #A=1/2*[x_1*y_2+x_2*y_3+x_3*y_1-x_2*y_1-x_3*y_2-x_1*y_3]# #A=1/2[(6, 3, 4, 6),(2, 5, 2, 2)]# #A=1/2*[6*5+3*2+4*2-3*2-4*5-6*2]# #A=1/[30+6+8-6-20-12]# #A=1/2(44-38)# #A=3" "#square units Now let's calculate the pyramid's volume V. #V=1/3*A*h# #V=1/3*3*8# #V=8" "#cubic units May God bless you all. I hope this explanation helps.

Sadie Adams · Answer

undefined To find the volume of a triangular pyramid, you can use the formula: Volume = (1/3) * base area * height.

First, find the area of the base triangle using the coordinates given for its vertices.

Using the formula for the area of a triangle: 
Area = (1/2) * base * height

Then, once you have the area of the base triangle and the height of the pyramid, plug these values into the volume formula.

Calculate the volume using the given values.