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Area of Elliptical Segment Formula

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Area of Elliptical Segment is the total quantity of plane enclosed by the boundary of the Elliptical Segment. Check FAQs

A Segment = (\frac{2a \cdot 2b}{4}) \cdot (\arccos (1 - (\frac{2 \cdot h Segment}{2a})) - (1 - (\frac{2 \cdot h Segment}{2a})) \cdot \sqrt{(\frac{4 \cdot h Segment}{2a}) - (\frac{4 \cdot {h Segment}^{2}}{{2a}^{2}})})

A_Segment - Area of Elliptical Segment?2a - Major Axis of Elliptical Segment?2b - Minor Axis of Elliptical Segment?h_Segment - Height of Elliptical Segment?

Area of Elliptical Segment Example

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Here is how the Area of Elliptical Segment equation looks like with Values.

Here is how the Area of Elliptical Segment equation looks like with Units.

Here is how the Area of Elliptical Segment equation looks like.

26.8377 = (\frac{20 \cdot 12}{4}) \cdot (\arccos (1 - (\frac{2 \cdot 4}{20})) - (1 - (\frac{2 \cdot 4}{20})) \cdot \sqrt{(\frac{4 \cdot 4}{20}) - (\frac{4 \cdot 4^{2}}{20^{2}})})

26.8377m² = (\frac{20m \cdot 12m}{4}) \cdot (\arccos (1 - (\frac{2 \cdot 4m}{20m})) - (1 - (\frac{2 \cdot 4m}{20m})) \cdot \sqrt{(\frac{4 \cdot 4m}{20m}) - (\frac{4 \cdot {4m}^{2}}{{20m}^{2}})})

26.8377 = (\frac{20 \cdot 12}{4}) \cdot (\arccos (1 - (\frac{2 \cdot 4}{20})) - (1 - (\frac{2 \cdot 4}{20})) \cdot \sqrt{(\frac{4 \cdot 4}{20}) - (\frac{4 \cdot 4^{2}}{20^{2}})})

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Area of Elliptical Segment Solution

Follow our step by step solution on how to calculate Area of Elliptical Segment?

FIRST Step Consider the formula

A Segment = (\frac{2a \cdot 2b}{4}) \cdot (\arccos (1 - (\frac{2 \cdot h Segment}{2a})) - (1 - (\frac{2 \cdot h Segment}{2a})) \cdot \sqrt{(\frac{4 \cdot h Segment}{2a}) - (\frac{4 \cdot {h Segment}^{2}}{{2a}^{2}})})

Next Step Substitute values of Variables

∴

A Segment = (\frac{20m \cdot 12m}{4}) \cdot (\arccos (1 - (\frac{2 \cdot 4m}{20m})) - (1 - (\frac{2 \cdot 4m}{20m})) \cdot \sqrt{(\frac{4 \cdot 4m}{20m}) - (\frac{4 \cdot {4m}^{2}}{{20m}^{2}})})

Next Step Prepare to Evaluate

∴

A Segment = (\frac{20 \cdot 12}{4}) \cdot (\arccos (1 - (\frac{2 \cdot 4}{20})) - (1 - (\frac{2 \cdot 4}{20})) \cdot \sqrt{(\frac{4 \cdot 4}{20}) - (\frac{4 \cdot 4^{2}}{20^{2}})})

Next Step Evaluate

∴

A Segment = 26.8377130800967m²

LAST Step Rounding Answer

∴

A Segment = 26.8377m²

Area of Elliptical Segment Formula Elements

Variables

Functions

Area of Elliptical Segment

Area of Elliptical Segment is the total quantity of plane enclosed by the boundary of the Elliptical Segment.

Symbol: A_Segment

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Elliptical Segment

Major Axis of Elliptical Segment

Major Axis of Elliptical Segment is the chord passing through both the foci of the Ellipse from which the Elliptical Segment is cut.

Symbol: 2a

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Major Axis of Elliptical Segment

Minor Axis of Elliptical Segment

Minor Axis of Elliptical Segment is the length of the longest chord which is perpendicular to the line joining the foci of the Ellipse from which the Elliptical Segment is cut.

Symbol: 2b

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Minor Axis of Elliptical Segment

Height of Elliptical Segment

Height of Elliptical Segment is the maximum vertical distance from the base edge to the curved edge of the Elliptical Segment.

Symbol: h_Segment

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Elliptical Segment

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

arccos

Arccosine function, is the inverse function of the cosine function.It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio.

Syntax: arccos(Number)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Elliptical Segment category

Go Major Axis of Elliptical Segment

2a = 2 \cdot a Segment

Go Minor Axis of Elliptical Segment

2b = 2 \cdot b Segment

Go Semi Major Axis of Elliptical Segment

a Segment = \frac{2a}{2}

Go Semi Minor Axis of Elliptical Segment

b Segment = \frac{2b}{2}

How to Evaluate Area of Elliptical Segment?

Area of Elliptical Segment evaluator uses Area of Elliptical Segment = ((Major Axis of Elliptical Segment*Minor Axis of Elliptical Segment)/4)*(arccos(1-((2*Height of Elliptical Segment)/Major Axis of Elliptical Segment))-(1-((2*Height of Elliptical Segment)/Major Axis of Elliptical Segment))*sqrt(((4*Height of Elliptical Segment)/Major Axis of Elliptical Segment)-((4*Height of Elliptical Segment^2)/(Major Axis of Elliptical Segment^2)))) to evaluate the Area of Elliptical Segment, Area of Elliptical Segment formula is defined as the total quantity of plane enclosed by the boundary of the Elliptical Segment. Area of Elliptical Segment is denoted by A_Segment symbol.

How to evaluate Area of Elliptical Segment using this online evaluator? To use this online evaluator for Area of Elliptical Segment, enter Major Axis of Elliptical Segment (2a), Minor Axis of Elliptical Segment (2b) & Height of Elliptical Segment (h_Segment) and hit the calculate button.

FAQs on Area of Elliptical Segment

What is the formula to find Area of Elliptical Segment?

The formula of Area of Elliptical Segment is expressed as Area of Elliptical Segment = ((Major Axis of Elliptical Segment*Minor Axis of Elliptical Segment)/4)*(arccos(1-((2*Height of Elliptical Segment)/Major Axis of Elliptical Segment))-(1-((2*Height of Elliptical Segment)/Major Axis of Elliptical Segment))*sqrt(((4*Height of Elliptical Segment)/Major Axis of Elliptical Segment)-((4*Height of Elliptical Segment^2)/(Major Axis of Elliptical Segment^2)))). Here is an example- 26.83771 = ((20*12)/4)*(arccos(1-((2*4)/20))-(1-((2*4)/20))*sqrt(((4*4)/20)-((4*4^2)/(20^2)))).

How to calculate Area of Elliptical Segment?

With Major Axis of Elliptical Segment (2a), Minor Axis of Elliptical Segment (2b) & Height of Elliptical Segment (h_Segment) we can find Area of Elliptical Segment using the formula - Area of Elliptical Segment = ((Major Axis of Elliptical Segment*Minor Axis of Elliptical Segment)/4)*(arccos(1-((2*Height of Elliptical Segment)/Major Axis of Elliptical Segment))-(1-((2*Height of Elliptical Segment)/Major Axis of Elliptical Segment))*sqrt(((4*Height of Elliptical Segment)/Major Axis of Elliptical Segment)-((4*Height of Elliptical Segment^2)/(Major Axis of Elliptical Segment^2)))). This formula also uses Cosine (cos)Inverse Cosine (arccos), Square Root (sqrt) function(s).

Can the Area of Elliptical Segment be negative?

No, the Area of Elliptical Segment, measured in Area cannot be negative.

Which unit is used to measure Area of Elliptical Segment?

Area of Elliptical Segment is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Area of Elliptical Segment can be measured.

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Area of Elliptical Segment Formula

Area of Elliptical Segment Example

Area of Elliptical Segment Solution

Area of Elliptical Segment Formula Elements

Other formulas in Elliptical Segment category

How to Evaluate Area of Elliptical Segment?

FAQs on Area of Elliptical Segment

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