Question 1080607
given: {{{x = 2}}} and {{{y = 6}}} and  two equilateral triangles

You have two equilateral triangles (you know this since two of the three sides have a length of "{{{y}}}" in each triangle.

Both triangles are the same.

To get the area, we need to know the height. We know the base is {{{x=2}}}, but not the height. 

Altitude of the shaded isosceles triangle:
{{{h^2 = y^2 + (x/2)^2}}}

{{{h = sqrt(y^2 + (x/2)^2)}}}..........{{{x=2}}} and {{{y=6}}}

{{{h = sqrt(6^2 + (2/2)^2)}}}
{{{h = sqrt(36+ 1)}}}
{{{h = sqrt(37)}}}
{{{h = 6.08}}}


Surface area of the shaded one  isosceles triangle:

{{{A[1]= (1/2)hx}}}

Surface area of the whole shaded figure:
{{{A = 2A[1]}}}
so, 
{{{A =  2(1/2)hx}}}

{{{A = hx}}}.............plug in values for  {{{h = 6.08}}} and {{{x=2}}}

{{{A = 6.08*2}}}

{{{A = 12.16}}}