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# geometry

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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
+338
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$$(\frac{10-\sqrt{2}}{2})^2$$ is the area of the shaded reigon

Jul 14, 2020
#2
+1326
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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

Dragan  Jul 15, 2020
#3
+1130
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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