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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?

 

 Jul 14, 2020
 #1
avatar+338 
+4

\((\frac{10-\sqrt{2}}{2})^2\) is the area of the shaded reigon

 Jul 14, 2020
 #2
avatar+1326 
+1

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   smiley

Dragan  Jul 15, 2020
 #3
avatar+1130 
+1

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

 Jul 15, 2020

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