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The base of a triangular pyramid is a triangle with corners at #(1 ,4 )#, #(6 ,2 )#, and #(8 ,5 )#. If the pyramid has a height of #7 #, what is the pyramid's volume?

Answer 1

Mason Adams

#color (orange)("Volume of Pyramid " V_p = (1/3) A_t * h = 70/3 " cub. units"#

#A (1,4), B(6,2), C(8,5), h = 7#

#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) |1 (6-8) + 6 (5-4) + 8 (4-2)| = 10#

#color (orange)("Volume of Pyramid " V_p = (1/3) A_t * h = (1/3) * 10 * 7 = 70/3 " cub. units"#

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Answer 2

Caroline Aucoin

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

Volume = (1/3) × Base Area × Height

To find the base area of the triangular pyramid, first calculate the area of the base triangle using the formula for the area of a triangle:

Area = (1/2) × base × height

Then, substitute the values into the volume formula:

Volume = (1/3) × Base Area × Height

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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.