blue rectangle

Geometry Level 1

Identical circles with diameter of 2 are arranged as shown, what is the area of the blue rectangle.

2 + 6\sqrt{3}

12 + 12\sqrt{3}

6(2 + \sqrt{3})

24 - \sqrt{3}

1 solution

Theodore Sinclair
Apr 9, 2018

The length of the rectangle is clearly 3 diameters=6. If we create an equilateral triangle joining the centres of three circle, the height of it will be $\sqrt{2^{2}-1^{2}}=\sqrt{3}$

Therefore the width of the rectangle is $2 \sqrt{3}+2$

Multiplying the length and the width we get $12 + 12\sqrt{3}$

blue rectangle

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