SOLUTION: In the figure below, AXC and BXD are arcs with centers B and A respectively. ABCD is a square of side 14 cm. Calculate the area of the region CXD. {{{drawing(200,180,-5,19,-

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Question 1202027: In the figure below, AXC and BXD are arcs with centers B and A respectively.
ABCD is a square of side 14 cm. Calculate the area of the region CXD.


Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
In the figure below, AXC and BXD are arcs with centers B and A respectively.
ABCD is a square of side 14 cm. Calculate the area of the region CXD. 


Draw AX and BX.

 

Triangle ABX is an equilateral triangle because AX = AD = AB and
BX = BD = AB, so AX = BX = AB.  So angle BAX = 60o.

Area of triangle ABX is 

Angle DAX = 90o - angle XAB =  90o-30o =  60o

Area of sector ADX is 
Area of sector BCX is also 

Area of square ABCD is .

Area of region CXD = Area of square - Area of sector ADX - Area of sector BDX - Area of triangle ABX

Area of region CXD = 

That's about 8.594159412 cm2.

Edwin
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