Question

side length. what is the lateral area of the prism? 12x square inches 12x² square inches 36x square inches 36x² square inches

Explanation:

1. Assume the prism is a regular - triangular prism (since no other information is given about the prism, and for simplicity, we consider a common case). Let the side - length of the base triangle be \(x\) and the height of the prism be \(12\).

• The lateral area of a prism \(L\) is given by the formula \(L = Ph\), where \(P\) is the perimeter of the base and \(h\) is the height of the prism.
• For a regular triangular prism with side - length of the base triangle \(x\), the perimeter of the base \(P\) (a triangle) is \(P=3x\) (since the sum of the lengths of the three sides of an equilateral triangle with side - length \(x\) is \(3x\)).
• The height of the prism \(h = 12\).

1. Calculate the lateral area using the formula \(L = Ph\).

• Substitute \(P = 3x\) and \(h = 12\) into the formula \(L=Ph\).
• \(L=(3x)\times12=36x\).

Answer:

36x square inches