The base of a triangular pyramid is a triangle with corners at (6 ,7 )(6,7), (2 ,5 )(2,5), and (3 ,1 )(3,1). If the pyramid has a height of 5 5, what is the pyramid's volume?

1 Answer
sankarankalyanam
Jan 8, 2018

Volume of pyramid V_p = (1/3)( A_t * h) = color (blue)(15)Vp=(13)(At⋅h)=15

Explanation:

Volume of pyramid V_p = (1/3)( A_t * h) Vp=(13)(At⋅h)
Where A_tAt is the base area of the triangle and h is the height of the pyramid.

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Using shoelace formula,

A_t = (1/2) [(x1 - x3)(y2 - y1) - (x1 - x2)(y3-y1)]At=(12)[(x1−x3)(y2−y1)−(x1−x2)(y3−y1)]

A_t = (1/2){(6-3)(5-7) - (6-2)(1-7)} = (1/2)(-6 + 24) = 9At=(12){(6−3)(5−7)−(6−2)(1−7)}=(12)(−6+24)=9

V_p = (1/3) * 9 * 5 = color (blue)(15)Vp=(13)⋅9⋅5=15

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