SOLUTION: In the diagram below AEFD is a rectangle. G and H are midpoints of EK and FK respectively, and K is the midpoint of AD. Find the area of the shaded region, in m^2. Do the midpoint

Question 1151112: In the diagram below AEFD is a rectangle. G and H are midpoints of EK and FK respectively, and K is the midpoint of AD. Find the area of the shaded region, in m^2.
Do the midpoints signify anything about the triangles?
Diagram: https://imgur.com/a/tzySxdO''
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Triangles EKF and KDF are both isosceles right triangles. Given 26 as the length of EF, the length of KF is , and then the length of DF is

So the area of the rectangle is 26*13 = 338.

The area of triangle EKF is half the area of the rectangle, 169.

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.

So the area of triangle GKH is 169/4; and then the area of the shaded region is

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