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

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Answer 1 · 2016-04-06T09:43:51

Volume $=14 " "$ cubic units

We compute for the area of the base which is a triangle first
Let $P_1(x_1, y_1)=(1, 2)$
Let $P_2(x_2, y_2)=(5, 2)$
Let $P_3(x_3, y_3)=(7, 5)$

Use the formula to compute for the area of the triangular base

Area $=1/2[(x_1,x_2,x_3,x_1),(y_1,y_2,y_3,y_1)]=1/2[(1,5,7,1),(2,2,5,2)]$

Area $=1/2*(x_1*y_2+x_2*y_3+x_3*y_1-x_2*y_1-x_3*y_2-x_1*y_3)$

Area $=1/2*(2+25+14-10-14-5)$

Area $=6$

Volume $=1/3*Area*height$

Volume $=1/3*6*7$

Volume $=14 " "$ cubic units

Answer 2 · 2016-04-06T09:46:47

$14" units"^3$

Tony B Tony B

Area of the base is $b/2xxa" "->" " 2xx3 = 6 " units"^2$

The volume of a triangular pyramid is:

$"base area" xx 1/3 xx "height"$

The height is given as 7

$color(blue)("base area" xx 1/3 xx "height " ->" " 6xx1/3xx7 =14 " units"^3$

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