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Aleonysh [2.5K]
2 years ago
9

Give the volume of the triangular prism shown

Mathematics
1 answer:
Nitella [24]2 years ago
6 0

Answer:

  D.  264 in³

Step-by-step explanation:

The missing edge dimension can be found using the Pythagorean theorem. Then the volume can be found using the appropriate formula.

<h3>Edge dimension</h3>

The missing dimension and the two given for the top triangle will satisfy the Pythagorean theorem. If the missing dimension is represented by 'a', then we have ...

  a² +8² = 10²

  a = √(100 -64) = 6 . . . . inches

<h3>Volume</h3>

The area of the top triangle is ...

  A = 1/2bh . . . . where b and h are the base and height dimensions

  A = 1/2(6 in)(8 in) = 24 in²

The volume of the triangular prism is ...

  A = Bh . . . . . where B is the area of the triangular base, and h is the prism height

  A = (24 in²)(11 in) = 264 in³

The volume of the triangular prism shown is 264 in³.

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