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The base of a triangular pyramid is a triangle with corners at #(3 ,8 )#, #(2 ,2 )#, and #(9 ,8 )#. If the pyramid has a height of #4 #, what is the pyramid's volume?

Answer 1

James Atkins

#color(blue)("Volume of pyramid " V_p = (1/3) * A_t * h = 24 " cub. units"#

#A (3,8), B (2,2), C (9,8), h = 4#

#"Area of base triangle " A-T = |(1/2)( x_1 (y_2-y_3) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2))|#

#A_t = |(1/2) (3 (2-8) + 2 (8-8) + 9 (8-2))| = 18#

#color(blue)("Volume of pyramid " V_p = (1/3) * A_t * h = (1/3) * 18 * 4 = 24#

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Answer 2

James Atkins

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

Volume = (1/3) * Area of Base * Height

First, calculate the area of the base triangle using the coordinates provided. You can use the formula for the area of a triangle given its vertices:

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

Then, substitute the values into the formula to find the volume:

Volume = (1/3) * Area of Base * Height

Once you have calculated the area of the base triangle and the 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.