Question

PLEASE ANSWER!!!!!! REALLY IMPORTANT
A prism has 2 congruent hexagonal bases like the one shown. Each hexagon is made from 2 congruent isosceles trapezoids.





The volume of the prism is 234 cubic units. What is the height of the prism?


3 units

4 units

6 units

8 units

Answer 1

Answer-

The height of the prism is 6 units

Solution-

As the base of the prism is a hexagon consisting of 2 congruent isosceles trapezoids.

So,

$V_{Prism}=Area_{Base}\times Height$

And,

$Area_{Base}=2\times \text{Area of the trapezoid}$

Also,

$\text{Area of the trapezoid}=\dfrac{1}{2}\times \text{Height}\times (\text{Sum of two parallel lines})$

$=\dfrac{1}{2}\times 3\times (5+8)\\\\=\dfrac{39}{2}$

Putting all the values,

$V_{Prism}=2\times \dfrac{39}{2}\times Height=39\times Height$

As the volume is given, so

$\Rightarrow 39\times Height=234$

$\Rightarrow Height=\dfrac{234}{39}=6$

Answer 2

Answer: Third option is correct.

Step-by-step explanation:

Since we have given that

Height of trapezium = 3 units

and Length of parallel sides are 5 units ad 4+4=8 units.

So, Area of trapezium is given by

$\dfrac{1}{2}\times \text{Sum of parallel sides}\times height\\\\=\dfrac{1}{2}\times (5+8)\times 3\\\\=\dfrac{1}{2}\times 13\times 3\\\\=19.5\ sq.\ units$

So, we have given that "Volume of prism = 234 cubic units":

$\text{Volume of prism}=\text{Area of base}\times height\\\\234=2\times \text{Area of trapezium}\times height\\\\234=2\times 19.5\times height\\\\234=39\times height\\\\height=\dfrac{234}{39}\\\\height=6\ units$

Hence, height of prism should be 6 units.

Thus, Third option is correct.