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,-

Algebra ->  Finance -> 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,-      Log On


   

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) About Me  (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 expr%281%2F2%29AX%2AAB%2Asin%2860%5Eo%29%22%22=%22%22expr%281%2F2%2914%2A14%2Aexpr%28srt%283%29%2F2%29%22%22=%22%2249sqrt%283%29

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

Area of sector ADX is expr%2830%5Eo%2F360%5Eo%29%2Api%2A14%5E249pi%2F3
Area of sector BCX is also 49pi%2F3

Area of square ABCD is 14%5E2%22%22=%22%22196.

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

Area of region CXD = 196-49pi%2F3-49pi%2F3-49sqrt%283%29%22%22=%22%22196-98pi%2F3-49sqrt%283%29

That's about 8.594159412 cm2.

Edwin