Let ABCD be a square of side 20 cm. The area of the square PQRS (in cm(square)) interior to ABCD, shown in the figure is?
\((\frac{10-\sqrt{2}}{2})^2\) is the area of the shaded reigon
Angle DAN = arctan( 10/20 ) = 26.565º
AP = PS = PQ = cos (26.565º) * 10 = 8.94427191
The area of a square PQRS = PS * PQ = 80 cm2
we find that the triangles made with 2 pieces is the same area as the square so the area is (10*2)^2/5=20^2/5=400/5=80
