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: Volume formula for prism

The volume formula for any prism is \(V = B\times h\), where \(B\) is the base area and \(h\) is the height. Given \(B = 15\) sq.in and \(h=3\) in, so \(V=(15)(3)\).

Step2: Unit of volume

Since the base area is in square inches (\(in^{2}\)) and height is in inches (\(in\)), the unit of volume \(V=(in^{2})\times in=in^{3}\) (cubic inches).

Step3: Analyze wrong statements

• For the statement “The volume cannot be determined because the dimensions of the base are unknown”: We know the base area \(B = 15\) sq.in, and using \(V=B\times h\), we can find the volume.
• For the statement “The edge length can be used in place of the height of an oblique prism if the height is unknown”: The edge length (slant - height) and the perpendicular height are different in an oblique prism. We use the perpendicular height (\(h = 3\) in here) for volume calculation.
• For the statement “The edge length times the height is the area of the base in any prism”: The area of the base \(B\) is given as 15 sq.in. In general, \(B\) is calculated based on the shape of the base (for a pentagon, \(B=\frac{1}{4}\sqrt{5(5 + 2\sqrt{5})}s^{2}\) where \(s\) is the side - length of the regular pentagon, but here we are directly given \(B\)). And \(edge\ length\times height\) has no relation to the base - area formula.

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.