SOLUTION: ABC is an equilateral triangle with sides of length 8 cm. Arc- AB, Arc-AC and Arc- BC are arcs of circles having their centres at C, B and A respectively. Find the total area of th

Algebra ->  Surface-area -> SOLUTION: ABC is an equilateral triangle with sides of length 8 cm. Arc- AB, Arc-AC and Arc- BC are arcs of circles having their centres at C, B and A respectively. Find the total area of th      Log On


   

Question 1208984: ABC is an equilateral triangle with sides of length 8 cm. Arc- AB, Arc-AC and Arc- BC are arcs of circles having their centres at C, B and A respectively. Find the total area of the non-shaded region of the diagram, in cm2.
https://ibb.co/pyVMjVQ
Answer by ikleyn(52803) About Me  (Show Source):
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ABC is an equilateral triangle with sides of length 8 cm. Arc- AB, Arc-AC and Arc- BC are arcs
of circles having their centres at C, B and A respectively.
Find the total area of the non-shaded region of the diagram, in cm2.
https://ibb.co/pyVMjVQ
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

The non-shaded area consists of three disjoint congruent shapes.


For each shape, its area is 1/6 of the area of the circle with the radius of 8 cm
minus the area of the equilateral triangle with the side of 8 cm.


So, the non-shaded area is  


      3%2A%281%2F6%29%2Api%2A8%5E2+-+3%2A8%5E2%2A%28sqrt%283%29%2F4%29 =  %281%2F2%29%2A64%2Api+-+3%2A64%2A%28sqrt%283%29%2F4%29 = 32%2Api-3%2A16%2Asqrt%283%29 = 


    = 32%2A3.14159-48%2Asqrt%283%29 = 17.39244  cm^2  (rounded).    ANSWER

Solved.