<u>Answer-</u>
<em>The height of the prism is</em><em> 6 units</em>
<u>Solution-</u>
As the base of the prism is a hexagon consisting of 2 congruent isosceles trapezoids.
So,
![V_{Prism}=Area_{Base}\times Height](https://tex.z-dn.net/?f=V_%7BPrism%7D%3DArea_%7BBase%7D%5Ctimes%20Height)
And,
![Area_{Base}=2\times \text{Area of the trapezoid}](https://tex.z-dn.net/?f=Area_%7BBase%7D%3D2%5Ctimes%20%5Ctext%7BArea%20of%20the%20trapezoid%7D)
Also,
![\text{Area of the trapezoid}=\dfrac{1}{2}\times \text{Height}\times (\text{Sum of two parallel lines})](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20the%20trapezoid%7D%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%20%5Ctext%7BHeight%7D%5Ctimes%20%28%5Ctext%7BSum%20of%20two%20parallel%20lines%7D%29)
![=\dfrac{1}{2}\times 3\times (5+8)\\\\=\dfrac{39}{2}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%203%5Ctimes%20%285%2B8%29%5C%5C%5C%5C%3D%5Cdfrac%7B39%7D%7B2%7D)
Putting all the values,
![V_{Prism}=2\times \dfrac{39}{2}\times Height=39\times Height](https://tex.z-dn.net/?f=V_%7BPrism%7D%3D2%5Ctimes%20%5Cdfrac%7B39%7D%7B2%7D%5Ctimes%20Height%3D39%5Ctimes%20Height)
As the volume is given, so
![\Rightarrow 39\times Height=234](https://tex.z-dn.net/?f=%5CRightarrow%2039%5Ctimes%20Height%3D234)
![\Rightarrow Height=\dfrac{234}{39}=6](https://tex.z-dn.net/?f=%5CRightarrow%20Height%3D%5Cdfrac%7B234%7D%7B39%7D%3D6)
Answer:34
Step-by-step explanation:
The volume of the refrigerator would be 30