Respuesta :
Triangular prism has 4 sides, including the base. The lateral area of the considered triangular prism is given by option B: [tex]12x^2 \: \rm inch^2[/tex]
How to find the lateral area of a triangular prism?
Lateral area of the considered triangular prism is the sum of areas of the triangles it is made up from except that of the base triangle.
The lateral area of a right prism which is regular (all lateral sides congruent) is given by:
[tex]A_L = P \times h[/tex]
where, P = Perimeter of the base
h = height of that prism
For the given case, we have the base of the triangular prism of side length x units.
Thus, perimeter of the base = x + x + x = 3x
Height of the base = h = 4 times x = 4x
Thus, we get:
Lateral area of the prism = [tex]3x \times 4x = 12x^2 \: \rm inch^2[/tex]
Thus, The lateral area of the considered triangular prism is given by option B: [tex]12x^2 \: \rm inch^2[/tex]
Learn more about lateral surface area of a prism here:
https://brainly.com/question/9656717
