Question

The figure below is an oblique triangular prism.

An oblique triangular prism is shown. Triangles A B C and F E D are the triangular bases. A bisector is drawn from point E to a point on side F D. LIne F D is extended to form a right angle with a line drawn from point C with length 2. The length of F D is x squared + 3 and the height of the bisector is x. The length of A F is 2 x.

The expression below represents the volume of the figure written in standard form. What are the missing values?

axb + cx

a =

b =

c =

Answer 1

Base area = 1/2 · FD · (height from E) = 1/2 · (x^2+3) · x. The prism height is 2, so volume = 2 · 1/2 · (x^2+3) · x = x(x^2+3) = x^3+3x.

Thus a = 1, b = 3, c = 3.