find the area of the shaded region.

If we look at the  small  right triangle on the bottom left of the  kite, it has a hypotenuse of 13 and a leg of 12....so...the height of the triangle is the other leg  and  is found as

√ [ 13^2  - 12^2 ] = √ [169 - 144]   = √25  = 5

So...by symmetry, we have two  congruent triangles comprising the top and bottom of the figure

The height of both triangles is 5 and the base is  12 + 8  = 20

So....the area of  one of the triangles is  (1/2) (5) (20)  =   50

And doubling this gives  the total area  of  100 units^2