SOLUTION: ABCD is a square with sides 4 cm. Arcs of radius 4 cm are drawn with centres at B and D. Find the area of the shaded region, in cm2. https://ibb.co/QNyNx4J

Algebra ->  Surface-area -> SOLUTION: ABCD is a square with sides 4 cm. Arcs of radius 4 cm are drawn with centres at B and D. Find the area of the shaded region, in cm2. https://ibb.co/QNyNx4J      Log On


   



Question 1209171: ABCD is a square with sides 4 cm. Arcs of radius 4 cm are drawn with centres at B and D. Find the area of the shaded region, in cm2.
https://ibb.co/QNyNx4J

Answer by ikleyn(52810) About Me  (Show Source):
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ABCD is a square with sides 4 cm. Arcs of radius 4 cm are drawn with centres at B and D.
Find the area of the shaded region, in cm2.
https://ibb.co/QNyNx4J
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Draw the diagonal AC.  It cuts the shaded area in two congruent parts of equal areas.
Each part is a quarter of the circle of the radius 4 cm minus the area of the isosceles
right angle triangle with the leg size of 4 cm.


So, the shaded area is  

    2%2A%28%281%2F4%29%2Api%2A4%5E2+-+%281%2F2%29%2A4%5E2%29 = 8%2Api-8 = 8*3.14159265-16 = 9.132741cm^2.    ANSWER

Solved.