Question

The base of a triangular pyramid is a triangle with corners at `(4 ,8 )`, `(6 ,7 )`, and `(2 ,3 )`. If the pyramid has a height of `15`, what is the pyramid's volume?

Answer 1

45

Explanation:

Area=`1/2*∣x_Ay_B+x_By_C+x_Cy_A−x_Ay_C−x_Cy_B−x_By_A∣`
`1/2*|4*7+6*3+2*8-4*3-2*7-6*3|`
`1/2*28+18+16-12-14-18`
`1/2*18`
base area = `9`
area of a pyramid = `(A_(base)*h)/3`
`9*15*1/3 = 45`