The base of a triangular pyramid is a triangle with corners at (5 ,8 )(5,8), (4 ,1 )(4,1), and (9 ,3 )(9,3). If the pyramid has a height of 4 4, what is the pyramid's volume?

1 Answer
Binayaka C.
Feb 11, 2018

Volume of the pyramid is 2222 cubic.unit .

Explanation:

Volume of a pyramid is 1/3*13⋅base area *⋅hight.

(x_1,y_1)=(5,8) ,(x_2,y_2)=(4,1),(x_3,y_3)=(9,3) , h=4(x1,y1)=(5,8),(x2,y2)=(4,1),(x3,y3)=(9,3),h=4

Area of Triangle is A_b =|1/2(x1(y2−y3)+x2(y3−y1)+x3(y1−y2))|Ab=∣∣∣12(x1(y2−y3)+x2(y3−y1)+x3(y1−y2))∣∣∣

A_b = |1/2(5(1−3)+4(3−8)+9(8−1))|Ab=∣∣∣12(5(1−3)+4(3−8)+9(8−1))∣∣∣ or

A_b = |1/2(-10-20+63)| = | 33/2| =16.5Ab=∣∣∣12(−10−20+63)∣∣∣=∣∣∣332∣∣∣=16.5sq.unit.

Volume of a pyramid is 1/3*A_b*h = 1/3*33/2*4 = 2213⋅Ab⋅h=13⋅332⋅4=22 cubic.unit
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