Answer
9.80
Work Step by Step
We can view the shaded figure as two congruent triangles. In order to find the area of the figure we can find the area of one of the triangles, and multiply our answer by two.
In order to use Heron's Formula to find the area of one of the triangles, we have to find the its semiperimeter:
$s=\frac{1}{2}(a+b+c)$
$s=\frac{1}{2}(2+5+5)$
$s=\frac{1}{2}*12$
$s=6$
We can use Heron's Formula from here to find the area of one of the triangles:
$A_{triangle}=\sqrt{s(s-a)(s-b)(s-c)}$
$A_{triangle}=\sqrt{6*(6-2)(6-5)(6-5)}$
$A_{triangle}=\sqrt{6*4*1*1}$
$A_{triangle}=\sqrt{24}$
$A_{triangle}=2\sqrt 6$
So each of the two triangles has an area of $2\sqrt 6$. The area of the shaded figure is twice that number:
$A=2*2\sqrt 6$
$A=4\sqrt 6$
$A\approx 9.80$
