The base of a triangular pyramid is a triangle with corners at (2 ,5 )(2,5), (1 ,6 )(1,6), and (2 ,8 )(2,8). If the pyramid has a height of 4 4, what is the pyramid's volume?

1 Answer
Binayaka C.
Jul 12, 2017

Volume of a pyramid is 2 2 cubic unit.

Explanation:

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

(x_1,y_1)=(2,5) ,(x_2,y_2)=(1,6),(x_3,y_3)=(2,8) , h=4(x1,y1)=(2,5),(x2,y2)=(1,6),(x3,y3)=(2,8),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(2(6−8)+1(8−5)+2(5−6))|Ab=∣∣∣12(2(6−8)+1(8−5)+2(5−6))∣∣∣ or

A_b = |1/2(-4+3-2)| = | -3/2| =3/2Ab=∣∣∣12(−4+3−2)∣∣∣=∣∣∣−32∣∣∣=32sq.unit

Volume of a pyramid is 1/3*A_b*h = 1/cancel3 *cancel3/2*4 = 2 cubic.unit [Ans]

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