Two circles have the same radius of 1cm. B & C are the center of the two circles.they have Intersected at A & D point.what is the area of ABCD?

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The both circles have the same radius of 1cm. B & C are the center of the two circles.they have Intersected at A & D point.what is the area of ABCD?

1 Answer
Shwetank Mauria
May 28, 2017

Area of ABCD is #1.2284# #cm^2#

Explanation:

Observe that #AB=AC=CD=BD# and hence #DeltaABC and #DeltaBCD# are two equilateral triangles.

Hence #/_ACD=/_ABD=120^@#

Now if we join #AD# it divides the desired area of ABCD in two equal segments
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and area of each segment, say ABD, is area of respective sector with angle #120^@# minus area of triangle #DeltaACD#.

Area of sector is #pixx1^2xx120^@/360^@=pi/3#

and area of #DeltaACD=1/2xx(2xxsqrt3/2)xx1/2=sqrt3/4#

(Note that #AD=2xxsqrt3/2# forms base of triangle and height is half of #BC# i.e. #1/2#)

Hence area of ABCD iss #2xx(pi/3-sqrt3/4)#

= #2xx(1.0472-0.4330)=2xx0.6142=1.2284# #cm^2#

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