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The figure above shows three consecutive squares of sides 5, 4 and 3, respectively.

 

Find the area of the black region.

 

 Dec 1, 2019
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Extend the side of 3 x 3 square 2 units up and draw a straight line to the left to connect it to the right corner of 5 x 5 square. Now, you have a rectangle with sides 5 x [5 + 4 +3] = 5 x 12 =60 sq. units. Half of it  is 60/2 =30 sq units, which is the area of the white right triangle with 5, 4, 3 units at the bottom. But the area of the 3 squares is:[3 x 3] + [4 x 4] + [5 x 5] =50 sq. units. So, the black area =50 - 30[The area of right triangle] =20 sq. units.

 Dec 1, 2019

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