Squares around square

Geometry Level 3

The area of the black square is 16.

The area of each smaller square (colored yellow, orange, dark blue, green) is 4.

Which area is larger, the red or the light blue?

Can't be determined The light blue area They are equal The red area

Áron Bán-Szabó by Áron Bán-Szabó , 17, Hungary

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2 solutions

Estella Z.
Oct 28, 2017

The large black square is 16 and the small squares added up are also 16. Every white part is taken out of both the red and the blue, therefore the red and the blue are equal.

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Steven Yuan
Aug 17, 2017

Let R R = area of red, W W = area of white, and B B = area of blue. The red and white regions combined form the four smaller squares, which has combined area 4 ( 4 ) = 16. 4(4) = 16. The white and blue regions combined form the larger square, which has area 16. Thus, the area of red and white equals the area of white and blue, or R + W = W + B . R + W = W + B. Therefore, R = B . ■ R = B. \, \blacksquare

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