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3 years ago

I NEED HELP PLEASE! :)

Mathematics

1 answer:

Mariana [72]3 years ago

5 0

Answer:

A. The volume of the prism = 204.7 cm³

Step-by-step explanation:

The difficult part is finding the hight x in the triangle with sides 6 6 and 7.

The half of the base of this triangle = 3,5

So we have the right sided triangle with a hypothenusa of 6, one right side of 3,5 and one right side which is x (and is unknown).

Use Pythagoras to find the value of x.

x² + (3,5)² = 6²

x² = 6² - (3,5)²

x² = 36 - 12,25

x² = 23.75

x = +- SQRT(23.75)

{Only the positive part has a meaning.}

x = 4.873

So now it is easy.

The area of the triangle = 3.5 * x

with x = 4.873

The area of the triangle = 3.5 * 4.873

The area of the triangle = 17.06 cm²

The volume of the prism = 12 * the area of the triangle

The volume of the prism = 12 * 17.06

The volume of the prism = 204.67

rounded on 1 decimal.

The volume of the prism = 204.7 cm³

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According to the theorem of sinuses :

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$Multiply \: both \: sides \: by \: \frac{ \sqrt{3} }{2}$

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_________________________________

I think this is the correct answer.

And we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️♥️

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