The base of a triangular pyramid is a triangle with corners at (5 ,8 )(5,8), (6 ,7 )(6,7), and (2 ,3 )(2,3). If the pyramid has a height of 15 15, what is the pyramid's volume?

1 Answer
Feb 24, 2018

The volume of the pyramid is 20 20 cubic units.

Explanation:

The volume of a pyramid is given by 1/3*13base area *height.

(x_1,y_1)-=(5,8) ,(x_2,y_2)-=(6,7),(x_3,y_3)-=(2,3) , h=15(x1,y1)(5,8),(x2,y2)(6,7),(x3,y3)(2,3),h=15

Area of Triangle is

A_b = |1/2(x_1(y_2−y_3)+x_2(y_3−y_1)+x_3(y_1−y_2))|Ab=12(x1(y2y3)+x2(y3y1)+x3(y1y2))

A_b = |1/2(5(7−3)+6(3−8)+2(8−7))| or

A_b = |1/2(20-30+2)| = | -8/2| =4 sq.unit.

So, the volume of the pyramid is 1/3*A_b*h = 1/3 *4*15 = 20 cubic units. [Ans]