Question

the base area of an oblique pentagonal prism is 15 sq. in. the prism measures 3 inches in height and the edges connecting the bases measure 5 inches each. which statements about the prism are true? check all that apply. the volume of the prism is computed using the expression (15)(3). the volume cannot be determined because the dimensions of the base are unknown. the edge length can be used in place of the height of an oblique prism if the height is unknown. the unit on the volume measure of the prism is cubic inches. the edge length times the height is the area of the base in any prism.

Explanation:

Step1: Recall prism volume formula

The volume \( V \) of any prism (including oblique prisms) is given by:
$$V = \text{Base Area} \times \text{Height}$$

Step2: Evaluate first statement

Given base area = 15 sq. in., height = 3 in. Substitute into formula:
$$V = 15 \times 3$$
This matches the expression in the first statement, so it is true.

Step3: Evaluate second statement

We have the base area and height, so volume can be calculated. The second statement is false.

Step4: Evaluate third statement

For oblique prisms, the slant edge length is not equal to the perpendicular height, so it cannot replace the height. This statement is false.

Step5: Evaluate fourth statement

Volume is measured in cubic units; since the linear units are inches, volume is cubic inches. This statement is true.

Step6: Evaluate fifth statement

Base area is independent of edge length and height; the product of edge length and height does not equal base area. This statement is false.

Answer:

• The volume of the prism is computed using the expression (15)(3).
• The unit on the volume measure of the prism is cubic inches.