Answer:
The volume of the triangular prism is 51.84 cm^3.
Step-by-step explanation:
The formula of the volume of a prism is:
V = Ah
where:
V = Volume of prism
A = Area of uniform cross-section or base of prism
h = Height of prism = 6 cm
We can substitute the information given in the problem into this formula.
To find A, we need to find the area of the triangular base.
A = bh / 2
where:
b = Base of triangle = 5.4 cm
h = Perpendicular height of triangle = 3.2 cm
We can substitute the information given in the problem into this formula.
A = ( 5.4 × 3.2 ) / 2
A = 17.28 / 2
A = 8.64 cm^2
Substitute the value of A into the original volume of a prism formula with the other information given in the problem.
V = Ah
V = ( 8.64 ) ( 6 )
V = 51.84 cm^3
The volume of the triangular prism when the base and the height is given so it should be [tex]51.84\ cm^3.[/tex]
Since The base of the triangular face is 5.4 centimeters and the height of the face is 3.2 centimeters. The height of the prism is 6 centimeters.
So, we know that
The formula of the volume of a prism is:
V = Ah
Here,
V = Volume of prism
A = Area
h = Height of prism = 6 cm
Also,
[tex]A = bh \div 2[/tex]
So,
[tex]A = ( 5.4 \times 3.2 ) \div 2\\\\= 17.28 \div 2\\\\= 8.64\ cm^2[/tex]
Now the volume is
V = Ah
V = ( 8.64 ) ( 6 )
V = [tex]51.84\ cm^3[/tex]
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