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nikitadnepr [17]
2 years ago
6

A triangular prism is 4 millimeters long. It has a triangular face with a base of 13 millimeters. The volume of the prism is 416

cubic millimeters. What is the height of its triangular face? Height = millimeters
Mathematics
2 answers:
Licemer1 [7]2 years ago
5 0

Answer:

h = 16 mm

Step-by-step explanation:

Th volume of the prism is:

V = A*l (1)

<u>Where:</u>

V. is the volume of the triangular prism = 416 mm³

A. is the area of the prism = ?

l: is the large of the prism = 4 mm

The area of the triangular face of the prism is:

A = \frac{1}{2}bh  (2)

<u>Where:</u>

b: is the base of the triangular face = 13 mm

h: is the height of the triangular face = ?

From equation (1) we have:

V = A*l

A = \frac{V}{l} = \frac{416 mm^{3}}{4 mm} = 104 mm^{2}

Now, using equation (2) we can find the height of the triangular face:

A = \frac{1}{2}bh

h = \frac{2A}{b} = \frac{2*104 mm^{2}}{13 mm} = 16 mm

Therefore, the height of the triangular face is 16 mm.

I hope it helps you!

muminat2 years ago
4 0

Answer:

16 millimeters

Step-by-step explanation:

  • Length of the Triangular Prism=4 millimeters
  • Base Length of One Triangular Face=13 millimeters.
  • Volume of the Prism =416 cubic millimeters.

Now:

Volume of a Prism=Base Area X Prism Length

Since we have a triangular base:

Volume of the Prism=(0.5 X Base X Height) X Prism Length

Substituting the given values, we obtain:

416=(0.5 X 13 X Height) X 4

416=26 X Height

Divide both sides by 26

Height of its triangular face=16 millimeters

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