Question

Find the volume of the triangular prism-shaped package that contains the sandwich.

Answer 1

`\mathrm {198 cm^(3)}`

Step-by-step explanation:

`\textrm {Volume of the sandwich :}`

`\mathrm {(1)/(2) * length * width * height}`

`\mathrm {(1)/(2) * 9 * 4 * 11}`

`\mathrm {2 * 99}`

`\mathrm {198 cm^(3)}`

Answer 2

Answer: 198

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Step-by-step explanation:

First we need the area of the triangular face.

area = base*height/2

area = 9*11/2

area = 99/2

area = 49.5 square cm

Multiply this triangular area with the depth of the prism.

volume = (area of base face)*(depth of prism)

volume = (49.5 sq cm)*4 cm)

volume = 198 cubic cm

The volume units "cubic cm" can be written as
`\text{cm}^3`

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Another way to think about it:

Consider a box that is 11 cm by 9 cm by 4 cm

The volume would be 11*9*4 = 396 cubic cm

That's for a rectangular prism, but we want a triangular prism. The volume will be half that at 396/2 = 198 cubic cm

If we had two identical triangular sandwiches, putting them together forms a full rectangular prism.