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: Third option is correct.

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

`(1)/(2)* \text{Sum of parallel sides}* height\\\\=(1)/(2)* (5+8)* 3\\\\=(1)/(2)* 13* 3\\\\=19.5\ sq.\ units`

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

`\text{Volume of prism}=\text{Area of base}* height\\\\234=2* \text{Area of trapezium}* height\\\\234=2* 19.5* height\\\\234=39* height\\\\height=(234)/(39)\\\\height=6\ units`

Hence, height of prism should be 6 units.

Thus, Third option is correct.

Answer 2

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)* Height`

And,

`Area_(Base)=2* \text{Area of the trapezoid}`

Also,

`\text{Area of the trapezoid}=(1)/(2)* \text{Height}* (\text{Sum of two parallel lines})`

`=(1)/(2)* 3* (5+8)\\\\=(39)/(2)`

Putting all the values,

`V_(Prism)=2* (39)/(2)* Height=39* Height`

As the volume is given, so

`\Rightarrow 39* Height=234`

`\Rightarrow Height=(234)/(39)=6`