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I am clueless about how to solve this. Your help is appreciated. Thanks

  • $\begingroup$ Hint: the three squares have sides $\,x, 5-x, 5-2x\,$, and you know one certain point lies on the circle. $\endgroup$
    – dxiv
    Mar 8, 2022 at 6:16
  • 1
    $\begingroup$ Too many questions begin or end with "I don't even know how to begin with this problem". While this may be true [...], it is still not a valid reason to limit your post to the statement of the problem without any mention of your own thoughts. – From Avoid "no clue" questions. $\endgroup$
    – Martin R
    Mar 8, 2022 at 6:23
  • $\begingroup$ Measleading figure.... $\endgroup$
    – dmtri
    Mar 8, 2022 at 7:07
  • 2
    $\begingroup$ Related (duplicate?): "Finding the total area of three squares". The question provides a solution to the problem above, but asks if what happens if the arc isn't assumed to be a semicircle. $\endgroup$
    – Blue
    Mar 8, 2022 at 7:46

1 Answer 1


Use coordinate geometry. Take left bottom point of green square as origin.

Side of green square: x

Side of gray square: 5-x

Side of blue square: (5-x)-x

Centre of circle: (2.5,0) Point on circle: (3x-5,x) Radius of circle: 2.5

Use distance formula: $(x-0)^2 + (3x-7.5)^2 = 2.5^2$ x = 2 (x = 2.5 discarded(?) )

Hence sides are 2, 3, 1 Area sum = 14

  • $\begingroup$ may i ask how do you get (3x-5,0)? $\endgroup$
    – Joe
    Mar 8, 2022 at 6:41
  • $\begingroup$ Side of green square - Side of blue square $\endgroup$ Mar 8, 2022 at 8:17

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