Clover like arcs

Geometry Level 3

Quadrilateral ABCD in the above diagram is a square with side length x = 27 cm x = 27 \text{ cm} . The arcs in the square are segments of circles with centers at the corners of the square. If the perimeter of the region bounded by the thick red curves is given to be k π k\pi , what is the value of k k ?


The answer is 18.

Shubh Gulati by Shubh Gulati , 25, India

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2 solutions

one side arc length=27 x pi/6; Total perimeter, k x pi= 4 x 27 x pi/6; => k=18

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Jai Jain
Jul 17, 2015

making an equilateral triangle from points B, C to the corner of the red bound figure, we can observe that the red segment on any arc=1/3 of the arc. This is because when drawing the triangle we also simultaneously create two 30 degree sectors. Now use ((PI*Diameter)/4) to calculate length of arc. Divide by 3 and multiply by 4 to get overall perimeter of red bound area. divide by Pi to get K=18

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