Question 388452
The lengths of the sides of the triangle are the sums of the respective radii.
{{{a=2+4=6}}}
{{{b=2+6=8}}}
{{{c=4+6=10}}}
Use Heron's formula,
{{{A=sqrt(s(s-a)(s-b)(s-c))}}}
where
{{{s=(a+b+c)/2}}}
{{{s=(6+8+10)/2}}}
{{{s=12}}}
Then,
{{{A=sqrt(12(12-6)(12-8)(12-10))}}}
{{{A=sqrt(12(6)(4)(2))}}}
{{{A=sqrt(144*4)}}}
{{{A=12*2}}}
{{{highlight(A=24)}}}