Question

The oblique prism below has an isosceles right triangle base.

An oblique right triangular prism is shown. The triangular bases have 2 sides with a length of x. The length of they hypotenuse is unknown. The distance from the 2 triangular bases is (x + 3). The vertical height of the prism is (x + 2).

What expression represents the volume of the prism, in cubic units?

One-halfx3 + x2
One-halfx3 + Three-halves x2
x3 + x2
x3 + 3x2

Answer 1

Volume = (area of triangular base) × (perpendicular height).
Base is an isosceles right triangle with legs x, so area = (1/2)x·x = (1/2)x^2. Use the vertical height (x + 2). Thus

V = (1/2)x^2(x + 2) = (1/2)x^3 + x^2.

So the correct expression is One-half x^3 + x^2.