Mixing
What is the area of this figure?
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I want to know how to find the area of this shape:
Yellow, white and blue shapes are ellipses.
Red is a square. The blue ellipse is not cut in half by the square.
I know that I have to add up all the areas, subtract the white ellipse, and then subtract portions of the othe elipses to find the area, yet I do not know how to determine the area of the portions I need to subtract. I would think of putting the figure in a grid, but still I do not know how to continue. Maybe using calculus, but is there a way to do this using geometry. Additionally I could make the blue ellipse be cut in half which would make my life easier.
calculus geometry area
asked Jan 18 at 23:30
Brian BlumbergBrian Blumberg
144113
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add a comment |
$begingroup$
I want to know how to find the area of this shape:
Yellow, white and blue shapes are ellipses.
Red is a square. The blue ellipse is not cut in half by the square.
I know that I have to add up all the areas, subtract the white ellipse, and then subtract portions of the othe elipses to find the area, yet I do not know how to determine the area of the portions I need to subtract. I would think of putting the figure in a grid, but still I do not know how to continue. Maybe using calculus, but is there a way to do this using geometry. Additionally I could make the blue ellipse be cut in half which would make my life easier.
calculus geometry area
asked Jan 18 at 23:30
Brian BlumbergBrian Blumberg
144113
$endgroup$
$begingroup$
Hint: the area if an ellipse is $pi ab$ where $a$ and $b$ are the semi-major and semi-minor axes.
$endgroup$
– John Douma
Jan 18 at 23:43
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I know that is the area of an ellipse, that is not the problem.
$endgroup$
– Brian Blumberg
Jan 18 at 23:46
1
$begingroup$
By "surface area" do you mean the standard area of your region? ("Surface area" usually refers to the area of a surface of a three-dimensional figure.) Are all the ellipses axis-aligned (the major and minor axes are all parallel or perpendicular to the squares sides)? Do you know the positions of all those figures in addition to their sizes?
$endgroup$
– Rory Daulton
Jan 19 at 0:38
add a comment |
$begingroup$
I want to know how to find the area of this shape:
Yellow, white and blue shapes are ellipses.
Red is a square. The blue ellipse is not cut in half by the square.
I know that I have to add up all the areas, subtract the white ellipse, and then subtract portions of the othe elipses to find the area, yet I do not know how to determine the area of the portions I need to subtract. I would think of putting the figure in a grid, but still I do not know how to continue. Maybe using calculus, but is there a way to do this using geometry. Additionally I could make the blue ellipse be cut in half which would make my life easier.
calculus geometry area
asked Jan 18 at 23:30
Brian BlumbergBrian Blumberg
144113
$endgroup$
I want to know how to find the area of this shape:
Yellow, white and blue shapes are ellipses.
Red is a square. The blue ellipse is not cut in half by the square.
I know that I have to add up all the areas, subtract the white ellipse, and then subtract portions of the othe elipses to find the area, yet I do not know how to determine the area of the portions I need to subtract. I would think of putting the figure in a grid, but still I do not know how to continue. Maybe using calculus, but is there a way to do this using geometry. Additionally I could make the blue ellipse be cut in half which would make my life easier.
calculus geometry area
calculus geometry area
asked Jan 18 at 23:30
Brian BlumbergBrian Blumberg
144113
asked Jan 18 at 23:30
Brian BlumbergBrian Blumberg
144113
edited Jan 19 at 1:41
Brian Blumberg
asked Jan 18 at 23:30
Brian BlumbergBrian Blumberg
144113
asked Jan 18 at 23:30
Brian BlumbergBrian Blumberg
144113
asked Jan 18 at 23:30
Brian BlumbergBrian Blumberg
144113
144113
$begingroup$
Hint: the area if an ellipse is $pi ab$ where $a$ and $b$ are the semi-major and semi-minor axes.
$endgroup$
– John Douma
Jan 18 at 23:43
$begingroup$
I know that is the area of an ellipse, that is not the problem.
$endgroup$
– Brian Blumberg
Jan 18 at 23:46
1
$begingroup$
By "surface area" do you mean the standard area of your region? ("Surface area" usually refers to the area of a surface of a three-dimensional figure.) Are all the ellipses axis-aligned (the major and minor axes are all parallel or perpendicular to the squares sides)? Do you know the positions of all those figures in addition to their sizes?
$endgroup$
– Rory Daulton
Jan 19 at 0:38
add a comment |
$begingroup$
Hint: the area if an ellipse is $pi ab$ where $a$ and $b$ are the semi-major and semi-minor axes.
$endgroup$
– John Douma
Jan 18 at 23:43
$begingroup$
I know that is the area of an ellipse, that is not the problem.
$endgroup$
– Brian Blumberg
Jan 18 at 23:46
1
$begingroup$
By "surface area" do you mean the standard area of your region? ("Surface area" usually refers to the area of a surface of a three-dimensional figure.) Are all the ellipses axis-aligned (the major and minor axes are all parallel or perpendicular to the squares sides)? Do you know the positions of all those figures in addition to their sizes?
$endgroup$
– Rory Daulton
Jan 19 at 0:38
$begingroup$
Hint: the area if an ellipse is $pi ab$ where $a$ and $b$ are the semi-major and semi-minor axes.
$endgroup$
– John Douma
Jan 18 at 23:43
$begingroup$
Hint: the area if an ellipse is $pi ab$ where $a$ and $b$ are the semi-major and semi-minor axes.
$endgroup$
– John Douma
Jan 18 at 23:43
$begingroup$
I know that is the area of an ellipse, that is not the problem.
$endgroup$
– Brian Blumberg
Jan 18 at 23:46
$begingroup$
I know that is the area of an ellipse, that is not the problem.
$endgroup$
– Brian Blumberg
Jan 18 at 23:46
1
1
$begingroup$
By "surface area" do you mean the standard area of your region? ("Surface area" usually refers to the area of a surface of a three-dimensional figure.) Are all the ellipses axis-aligned (the major and minor axes are all parallel or perpendicular to the squares sides)? Do you know the positions of all those figures in addition to their sizes?
$endgroup$
– Rory Daulton
Jan 19 at 0:38
$begingroup$
By "surface area" do you mean the standard area of your region? ("Surface area" usually refers to the area of a surface of a three-dimensional figure.) Are all the ellipses axis-aligned (the major and minor axes are all parallel or perpendicular to the squares sides)? Do you know the positions of all those figures in addition to their sizes?
$endgroup$
– Rory Daulton
Jan 19 at 0:38
add a comment |
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$begingroup$
Hint: the area if an ellipse is $pi ab$ where $a$ and $b$ are the semi-major and semi-minor axes.
$endgroup$
– John Douma
Jan 18 at 23:43
$begingroup$
I know that is the area of an ellipse, that is not the problem.
$endgroup$
– Brian Blumberg
Jan 18 at 23:46
1
$begingroup$
By "surface area" do you mean the standard area of your region? ("Surface area" usually refers to the area of a surface of a three-dimensional figure.) Are all the ellipses axis-aligned (the major and minor axes are all parallel or perpendicular to the squares sides)? Do you know the positions of all those figures in addition to their sizes?
$endgroup$
– Rory Daulton
Jan 19 at 0:38