The base of a triangular pyramid is a triangle with corners at #(3 ,7 )#, #(5 ,4 )#, and #(8 ,2 )#. If the pyramid has a height of #2 #, what is the pyramid's volume?

Question

The base of a triangular pyramid is a triangle with corners at #(3 ,7  )#, #(5  ,4   )#, and #(8  ,2  )#.  If the pyramid has a height of #2  #, what is the pyramid's volume?

Mason Adams · Accepted Answer

Volume of a pyramid is # 1 2/3 # cubic.unit [Ans]

Volume of a pyramid is #1/3*#base area #*#hight. Here The base triangle's corners and height are both specified. #(x_1,y_1)=(3,7) ,(x_2,y_2)=(5,4),(x_3,y_3)=(8,2) , h=2# Area of Triangle is #A_b = |1/2(x1(y2−y3)+x2(y3−y1)+x3(y1−y2))|# #A_b = |1/2(3(4−2)+5(2−7)+8(7−4))|# or #A_b = |1/2(6-25+24)| = | 5/2| =5/2 =2.5#sq.unit Volume of a pyramid is #1/3*A_b*h = 1/3 *2.5*2 = 5/3 = 1 2/3# cubic.unit [Ans]

James Atkins · Answer

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

$$ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} $$

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

Once you have the base area and the height (given as 2 units), plug these values into the formula for the volume of a pyramid and calculate it.