Mensa Basic Geometry Brain Twisters

 

1) The Rectangle Problem:

The height of a rectangle is 81 units. Two circles are inscribed in the rectangle as shown above. The circles are tangent to each other. A line segment has an endpoint on both circles and passes through the point of tangency. It measures 56 units, and is parallel to the height of the rectangle. What is the length L of the rectangle?

1) The Square Problem:   

ABCD is a square. W is the midpoint of AB.  Z is the center of the square where AD and BC intersect. X is the point where AD and WC intersect. Y is the point where BC and WD intersect.

If the area of square ABCD is 4 square units, then find the area of the orange region WYXZ.