Answer:
16 millimeters
Step-by-step explanation:
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
Answer:
h = 16 mm
Step-by-step explanation:
Th volume of the prism is:
[tex] V = A*l [/tex] (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:
[tex] A = \frac{1}{2}bh [/tex] (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:
[tex] V = A*l [/tex]
[tex] A = \frac{V}{l} = \frac{416 mm^{3}}{4 mm} = 104 mm^{2} [/tex]
Now, using equation (2) we can find the height of the triangular face:
[tex] A = \frac{1}{2}bh [/tex]
[tex] h = \frac{2A}{b} = \frac{2*104 mm^{2}}{13 mm} = 16 mm [/tex]
Therefore, the height of the triangular face is 16 mm.
I hope it helps you!
