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? A. The area of the cross-sections of the prisms are multiples of each other. B. The vertical cross-sections of the prisms at the same width must have the same area. C. The cross-sections of the prisms are the same shape. D. The horizontal cross-sections of the prisms at the same height must have the same area.

Answer 1

D. The horizontal cross-sections of the prisms at the same height must have the same area.

Explanation:

The formula for the volume of both the rectangular prism and the oblique triangular prism is:

`V=Ab*H`

Which is area of the base times the height, if they both have the same height then the area of the base must be the same, since the figures are different, as the base of one is rectangular and the other is a triangle, you can not have the same measurements for the width or the vertical crossed sections, since the area is distributed different.

Answer 2

The volume of a prism is the product obtained when multiplying the area of its base to its height. If the two given solid figures have the same volume and the same height then, the areas of their bases are also equal. Thus, the answer is letter D.