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The base of a triangular pyramid is a triangle with corners at #(3 ,7 )#, #(1 ,4 )#, and #(4 ,2 )#. If the pyramid has a height of #2 #, what is the pyramid's volume?

Answer 1

Sadie Allen

#"volume "=26/3#

#"the volume (V) of a pyramid is calculated using the formula"#

#•color(white)(x)V=1/3xx"area of base "xx" height"#

#"the area (A) of the triangle can be found using"#

#•color(white)(x)A=1/2|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|#

#"let "(x_1,y_1)=(3,7),(x_2,y_2)=(1,4),(x_3,y_3)=(4,2)#

#A=1/2|3(4-2)+1(2-7)+4(7-4)|#

#color(white)(A)=|6-5+12|=13#

#V=1/3xx13xx2=26/3#

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Answer 2

Allison Allen

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

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

First, calculate the area of the base triangle using the given coordinates. You can use the formula for the area of a triangle, which is:

[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} ]

After finding the base area, substitute it along with the given height into the volume formula to calculate 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.