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

1 Answer
Mar 26, 2018

5.67 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)}

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

(x_2,y_2) and (x_3,y_3) respectively.]

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

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

= 1/2(17) sq. units

= 8.5 sq. units.

So, The Volume of The Triangular Pyramid

= 1/3(ah) [Where a is the area of the base and h is the height of the pyramid.]

= 1/3 (8.5*2) cubic units

= 17/3 cubic units

=5.67 cubic units (approx.)

Hope this helps.