The base of a triangular pyramid is a triangle with corners at (3 ,7 )(3,7), (5 ,4 )(5,4), and (8 ,2 )(8,2). If the pyramid has a height of 2 2, what is the pyramid's volume?

1 Answer
Binayaka C.
Sep 22, 2017

Volume of a pyramid is 1 2/3 123 cubic.unit [Ans]

Explanation:

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

the corners of base triangle are given as well as height also.

(x_1,y_1)=(3,7) ,(x_2,y_2)=(5,4),(x_3,y_3)=(8,2) , h=2(x1,y1)=(3,7),(x2,y2)=(5,4),(x3,y3)=(8,2),h=2

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(3(4−2)+5(2−7)+8(7−4))|Ab=∣∣∣12(3(4−2)+5(2−7)+8(7−4))∣∣∣ or

A_b = |1/2(6-25+24)| = | 5/2| =5/2 =2.5Ab=∣∣∣12(6−25+24)∣∣∣=∣∣∣52∣∣∣=52=2.5sq.unit

Volume of a pyramid is 1/3*A_b*h = 1/3 *2.5*2 = 5/3 = 1 2/313⋅Ab⋅h=13⋅2.5⋅2=53=123

cubic.unit [Ans]

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