Question

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

Answer 1

Answer:

h = 16 mm

Step-by-step explanation:

Th volume of the prism is:

$V = A*l$ (1)

Where:

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)

Where:

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!

Answer 2

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