Option C) 48in³ is the correct answer.
Hence, the volume of the right triangular prism is 48in³.
This question is incomplete, the missing diagram is uploaded along this answer.
Given the data in the question;
- Side length a; [tex]a = 4in[/tex]
- Side length b; [tex]b = 5in[/tex]
- Side length c; [tex]c = 3in[/tex]
- Height; [tex]h = 8in[/tex]
Volume; [tex]V = \ ?[/tex]
Volume of right triangular Prism
Volume is simply the space created when a surface is enclosed , it is the space that a quantity material that can be held.
The volume of a right triangular prism can be expressed as;
[tex]V = \frac{1}{4}h\sqrt{(a+b+c)(b+c-a)(c+a-b)(a+b-c)}[/tex]
To determine the volume of the right triangular prism, we substitute our given values into the expression above.
[tex]V = \frac{1}{4}h\sqrt{(a+b+c)(b+c-a)(c+a-b)(a+b-c)}\\\\V = \frac{1}{4}*8in*\sqrt{(4in+5in+3in)(5in+3in-4in)(3in+4in-5in)(4in+5in-3in)}\\\\V = \frac{1}{4}*8in*\sqrt{(12in)(4in)(2in)(6in)}\\\\V = \frac{1}{4}*8in*\sqrt{576in^4}\\\\V = \frac{1}{4}*8in*24in^2\\\\V = \frac{1}{4} * 192in^3\\\\V = 48in^3[/tex]
Option C) 48in³ is the correct answer.
Hence, the volume of the right triangular prism is 48in³.
Learn more about volume of right triangular prism : https://brainly.com/question/17208216
