Question

A right rectangular prism and an oblique triangular prism are both 12 centimeters tall and have the same volume. What statement must be true about the two solids?

Answer 1

The volume of right rectangular prism is

`V_(rect)=A_(rectangle)\cdot H.`

The volume of an oblique triangular prism is

`V_(tr)=(1)/(3)\cdot A_(triangle) \cdot H.`

Since the height and the volume are the same, then

`A_(rectangle)=(1)/(3)\cdot A_(triangle) \text{ or } A_(triangle)=3A_(rectangle).`

Answer: statement that the area of triangle is three times the area of rectangle must be true.