Find the surface area and volume. show your work.

9514 1404 393

Answer:

Step-by-step explanation:

Surface area

The length of the hypotenuse of the front facing triangle is given by the Pythagorean theorem:

  d^2 = 13^2 +6^2 = 169 +36 = 205

  d = √205

So, the perimeter of that triangle is ...

  P = 13 +6 +√205 = 19 +√205

The total area of the rectangular faces of this triangular prism is then ...

  rectangular face area = (base perimeter)·(prism height)

  = (19 +√205)(7) = 133 +7√205

The area of the two triangular faces will be ...

  triangular face total area = 2·(triangle area) = 2(1/2)(6)(13) = 78

Then the total surface area is ...

  total surface area = rectangular face area + triangular face total area

  total surface area = (133 +7√205) +78

  surface area = 211 +7√205 ≈ 311.22 . . . . square units

__

Volume

The volume is the product of the area of the triangular base and the height of the prism.

  V = Bh

  V = (39)(7)

  volume = 273 . . . . cubic units

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