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Please find below the solution to the asked query:
Given : ABCD is a square and side of square = AB = 10.5
And we know area of square = ( Side )2 , So
Area of square ABCD = ( 10.5 )2 = 110.25 cm2
Also given : Circle with center ' O ' have its area is one fifth of area of square , So
Area of circle with center ' O ' = = 22.05
And diagonal of square AC and BD intersect at ' O ' , and we know diagonal of square bisect it to equal parts , So
Area of triangle ACD = 110.25 = 55.125 cm2
As diagonal AC passing through center ' o ' of given circle then that also bisect area of given circle , So
Area of half circle = 22.05 = 11.025 cm2
Then,
Area of shaded region = Area of triangle ACD - Area of half circle = 55.125 - 11.025 = 44.1 cm2 ( Ans )
We know : area of circle = r2 and we calculate area of circle with center ' O ' = 22.05 cm2 , So
r2 = 22.05 ( Here r = Radius of given circle )
We know perimeter of half circle ( Without diagonal ) = r , So
Perimeter of half circle with center ' O ' = 8.33 cm
Here , XY = Diameter of circle with center ' O ' = 2 ( 2.65 ) = 5.3 cm
And
We know diagonal of square = ( Side ) , So
Length of AC = ( 10.5 ) = 1.414 10.5 = 14.847 14.85 cm
Therefore ,
Perimeter of shaded region = AD + CD + AC - XY + Perimeter of half circle with center ' O ' , Substitute all values we get :
Perimeter of shaded region = 10.5 + 10.5 + 14.85 - 5.3 + 8.33 = 38.88 cm ( Ans )
Hope this information will clear your doubts about topic.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards
Please find below the solution to the asked query:
Given : ABCD is a square and side of square = AB = 10.5
And we know area of square = ( Side )2 , So
Area of square ABCD = ( 10.5 )2 = 110.25 cm2
Also given : Circle with center ' O ' have its area is one fifth of area of square , So
Area of circle with center ' O ' = = 22.05
And diagonal of square AC and BD intersect at ' O ' , and we know diagonal of square bisect it to equal parts , So
Area of triangle ACD = 110.25 = 55.125 cm2
As diagonal AC passing through center ' o ' of given circle then that also bisect area of given circle , So
Area of half circle = 22.05 = 11.025 cm2
Then,
Area of shaded region = Area of triangle ACD - Area of half circle = 55.125 - 11.025 = 44.1 cm2 ( Ans )
We know : area of circle = r2 and we calculate area of circle with center ' O ' = 22.05 cm2 , So
r2 = 22.05 ( Here r = Radius of given circle )
We know perimeter of half circle ( Without diagonal ) = r , So
Perimeter of half circle with center ' O ' = 8.33 cm
Here , XY = Diameter of circle with center ' O ' = 2 ( 2.65 ) = 5.3 cm
And
We know diagonal of square = ( Side ) , So
Length of AC = ( 10.5 ) = 1.414 10.5 = 14.847 14.85 cm
Therefore ,
Perimeter of shaded region = AD + CD + AC - XY + Perimeter of half circle with center ' O ' , Substitute all values we get :
Perimeter of shaded region = 10.5 + 10.5 + 14.85 - 5.3 + 8.33 = 38.88 cm ( Ans )
Hope this information will clear your doubts about topic.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards