The base of a triangular pyramid is a triangle with corners at (3 ,1 ), (4 ,9 ), and (5 ,7 ). If the pyramid has a height of 7 , what is the pyramid's volume?

1 Answer
Barney V.
Jan 12, 2018

11.69 units^3

Explanation:

sqrt((x_2-x_1)^2+(y_2-y_1)^2)

:.=sqrt((5-3)^2+(7-1)^2)

:.=sqrt((2)^2+(6)^2)

:.=sqrt((4)+(36))

:.=sqrt((4)+(36))

:.=sqrt(40)

side a=6.325units

:.=sqrt((4-3)^2+(9-1)^2)

:.=sqrt((1)^2+(8)^2)

:.=sqrt((1)+(64))

:.=sqrt(65)

side b=8.062units

:.=sqrt((5-4)^2+(7-9)^2)

:.=sqrt((1)^2+(2)^2)

:.=sqrt((1)+(4))

:.=sqrt(5)

side c=2.236

Hero's formula:-

Area of triangle=sqrt(s(s-a)(s-b)(s-c))

where s=(a+b+c)/2

:.s=(6.325+8.062+2.236)/2

:.s=16.623/2

:.s=8.312

:.=sqrt(8.312(8.312-6.325)(8.312-8.062)(8.312-2.236)))

:.=sqrt((8.312)(1.987)(0.25)(6.076))

:.=sqrt(25.08771894)

Area of triangle=5.01units^2

Volume of triangular prism=1/3AxxH

A=triangular base and H= height of pyramid

:.=1/3xx5.01xx7

:.=11.69 units^3

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