Find the area in sq. cm.

Geometry Level 2

If ABCD is a rectangle, the circles are congruent and the sides of the rectangle are tangent to the cirlcles , find the area of the red part.


The answer is 19.5039.

इश्वर बस्याल by इश्वर बस्याल , 19, Nepal

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1 solution

Given: ABCD is a rectangle E and F are centres of the circles. AB, AD, DC and BC are tangents. Construction: FG, HG and FI

  1. Area of the square FICH - Area of quarter FIH= Area of arc IHC. So, 5^2 - 19.64 = 5.36 sq. cm
  2. angle GJF = tan inverse(5/10) = 26.5 degrees
  3. angle GFH= 2 times angle GJF [ central angle and inscribed angle on same are arc relation] angle GFH = 53.13 degrees
  4. part GFH= (53.1/360)* 25 pi= 11.5911 cm^2

  5. Area of triangle JHB- JFG- arc GFH = GHB so, GHB=3.4088 cm^2

  6. Area of shaded part = 3 arc ICH + arc GHB = 19.50 cm ^2

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