SOLUTION: (49) In the diagram, ABCD is a unit square. Arc AC has center D and arc BD has center C. Find the shaded area in square units. Link to diagram: https://ibb.co/zhCbbmhz

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Question 1209525: (49) In the diagram, ABCD is a unit square. Arc AC has center D and arc BD has center C. Find the shaded area in square units.
Link to diagram: https://ibb.co/zhCbbmhz

Answer by ikleyn(52921)   (Show Source): You can put this solution on YOUR website!
.
(49) In the diagram, ABCD is a unit square. Arc AC has center D and arc BD has center C.
Find the shaded area in square units.
Link to diagram: https://ibb.co/zhCbbmhz
~~~~~~~~~~~~~~~~~~~~

The shaded area is the sum of areas of two 60°-degrees sectors of a circle of the radius of 1 unit

minus the area of the equilateral triangle with the side length of 1.


The area of one 60°-sector of a circle of the radius 1 is 1/6 of the area of the circle, i.e.

     = .


The area of the equilateral triangle with the side length 1 is  .


Therefore, the shaded area is  

     +  -  =  -  =  -  =  -  = 0.614184848  square units (approximately).


ANSWER.  The shaded area is   = 0.6142  square units (approximately).

Solved.



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