Question

he 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 base) × (perpendicular height). The base is an isosceles right triangle with legs x, so area = (1/2)x^2. The perpendicular (vertical) height is x + 2. Thus

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

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