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The base of a triangular pyramid is a triangle with corners at #(6 ,5 )#, #(2 ,2 )#, and #(4 ,7 )#. If the pyramid has a height of #8 #, what is the pyramid's volume?

Answer 1

Claire Akin

Volume #V=18 2/3=18.67" "#cubic units

To solve for the volume of the pyramid which is #V=1/3*area*height#

Solve for the area of the triangle first with #P_1(2, 2),P_2(6, 5),P_3(4, 7)#

the matrix for area A

#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*[(2,6,4,2),(2,5,7,2)]#

#A=1/2*[2(5)+6(7)+4(2)-6(2)-4(5)-2(7)]#

#A=1/2*(10+42+8-12-20-14)#

#A=1/2*(60-46)#

#A=7#

Here we have volume V.

#V=1/3*area*height#

#V=1/3*7*8=56/3#

#V=18 2/3#

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Answer 2

James Atkins

To find the volume of the triangular pyramid, you can use the formula:

[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} ]

First, calculate the area of the base triangle using the given coordinates.
Then, use the formula to find the volume by multiplying the base area by the height of the pyramid.

Once you have the base area and height, plug them into the formula to find the volume of the pyramid.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.