The base of a triangular pyramid is a triangle with corners at #(4 ,5 )#, #(6 ,7 )#, and #(7 ,3 )#. If the pyramid has a height of #15 #, what is the pyramid's volume?

Answer 1

#"volume "=25#

#"the volume (V) of a pyramid is calculated using the formula"#
#•color(white)(x)V=1/3xx"area of base "xx"height"#
# " the area of the triangle (A) can be found using"#
#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)=(4,5),(x_2,y_2)=(6,7),(x_3,y_3)=(7,3)#
#A=1/2|4(7-3)+6(3-5)+7(5-7)|#
#color(white)(A)=1/2|16-12-14|=1/2xx10=5#
#rArrV=1/3xx5xx15=25#
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Answer 2

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

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

First, calculate the area of the base triangle using the coordinates given:

Area of triangle = (1/2) * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the vertices of the triangle.

Using the given coordinates: (x1, y1) = (4, 5), (x2, y2) = (6, 7), and (x3, y3) = (7, 3)

Plug these values into the formula to find the area of the base triangle.

Then, once you have the area of the base triangle and the height of the pyramid, plug them into the volume formula to find the volume of the triangular 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.

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.

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.

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.

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