Question 33408
First, you can write:
{{{A = (k)(a)(p)}}}
To find the value of k, the constant of variation, substitute the given values of A, a, and p.
{{{46.8 = (k)(3)(31.2)}}} Solve for k.
{{{46.8 = 93.6(k)}}} Divide both sides by 93.6
{{{46.8/93.6 = k}}}
{{{k = 0.5}}} Constant of variation.

{{{A = 0.5ap}}} Joint variation equation.

{{{A = 0.5(2.3)(12)}}}
{{{A = 13.8}}}sq.ins.

There is a problem with answer!
If you calculate the area of the given regular (equilateral) triangle using Heron's formula{{{A = sqrt(s(s-a)(s-b)(s-c))}}}, you will get 6.9 sq.ins. which is just half of what I got using the direct variation method above.

I have concluded that the given apothem (a = 2.3 inches) is just twice what it should be for a regular triangle of 4 inches per side.

You might want to check this out.