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

1 Answer
Mar 26, 2018

5.675.67 cubic units

Explanation:

First Of All, Find the Area of the Triangular Base.

So, The Area of the Base of The Pyramid :-

1/2{x_1(y_2 -y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)}12{x1(y2y3)+x2(y3y1)+x3(y1y2)}

[If The Coordiantes for the vertices of the triangles are (x_1,y_1),(x1,y1),

(x_2,y_2) and (x_3,y_3)(x2,y2)and(x3,y3) respectively.]

= 1/2{2(3-2) + 5(2-7) + 8(7 - 3)}=12{2(32)+5(27)+8(73)} sq. units

= 1/2{2 -25 +40}=12{225+40} sq. units

= 1/2(17)=12(17) sq. units

= 8.5=8.5 sq. units.

So, The Volume of The Triangular Pyramid

= 1/3(ah)=13(ah) [Where aa is the area of the base and hh is the height of the pyramid.]

= 1/3 (8.5*2)=13(8.52) cubic units

= 17/3=173 cubic units

=5.67=5.67 cubic units (approx.)

Hope this helps.