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The base of a triangular pyramid is a triangle with corners at #(5 ,8 )#, #(4 ,3 )#, and #(9 ,4 )#. If the pyramid has a height of #4 #, what is the pyramid's volume?

Answer 1

Allison Allen

Volume of pyramid is #16# cubic unit.

#(x_1,y_1) = (5,8) ; (x_2,y_2) = (4,3) ; (x_3,y_3) = (9,4)#

Area of triangle with given vertices is #A_t=1/2(x_1(y_2-y_3) +x_2(y_3-y_1)+x_3(y_1-y_2) # or

#A_t=1/2(5(3-4) +4(4-8)+9(8-3)) = 1/2 (-5-16+45)=1/2*24=12# sq.unit

Given height of pyramid is #h=4#

Volume of a pyramid is #V=1/3*A_t*h= 1/3*12*4=16# cubic unit [Ans]

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Answer 2

Mason Adams

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

Volume = (1/3) * base area * height

First, calculate the area of the base triangle using the coordinates provided. Then, multiply the base area by the height of the pyramid and divide by 3 to find the volume.

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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.