Question

consider the right triangular prism given ac = 9 cm and ad = 10 cm. which statements are true regarding the prism? check all that apply. the height of the prism is 10 cm. △dfg is a base. △dfg is a lateral side. the appropriate unit of measure for the volume is cubic centimeters. the area of the base is 45 square centimeters.

Explanation:

Step1: Identify prism height

The length of the edge connecting the two triangular bases (AD) is the prism's height. Given $AD=10$ cm, so the height is 10 cm.

Step2: Identify base vs lateral side

The right triangular prism has triangular bases $\triangle ABC$ and $\triangle DFG$. $\triangle DFG$ is a base, not a lateral side.

Step3: Verify volume unit

All linear measurements are in centimeters, so volume (a 3D measure) uses cubic centimeters.

Step4: Check base area

We only know $AC=9$ cm, the right angle is at A, but we do NOT know the length of the other leg of the right triangle base. We cannot calculate the base area as 45 cm² with the given information.

Answer:

• The height of the prism is 10 cm.
• $\Delta$DFG is a base.
• The appropriate unit of measure for the volume is cubic centimeters.