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vova2212 [387]
3 years ago
7

PLEASE ANSWER!!!!!! REALLY IMPORTANT

Mathematics
2 answers:
faust18 [17]3 years ago
8 0

<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

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

Alisiya [41]3 years ago
7 0

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.

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\mathrm{Hope\:This\:Helps!!!}

\mathrm{-Austint1414}

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