Question 1151112
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Triangles EKF and KDF are both isosceles right triangles.  Given 26 as the length of EF, the length of KF is {{{26/sqrt(2)}}}, and then the length of DF is {{{(26/sqrt(2))/sqrt(2) = 26/2 = 13}}}<br>
So the area of the rectangle is 26*13 = 338.<br>
The area of triangle EKF is half the area of the rectangle, 169.<br>
Because G and H are the midpoints of KE and KF, triangles GKH and EKF are similar with a ratio of 1:2.  That means the ratio of the areas of those triangles is 1:4.<br>
So the area of triangle GKH is 169/4; and then the area of the shaded region is {{{169-169/4 = 507/4}}}<br>