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Area of Elliptical Sector Formula

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

A Sec = (\frac{a Sector \cdot b Sector}{2}) \cdot (∠ Sector - a \tan (\frac{(b Sector - a Sector) \cdot \sin (2 \cdot ∠ Leg(2))}{a Sector + b Sector + ((b Sector - a Sector) \cdot \cos (2 \cdot ∠ Leg(2)))}) + a \tan (\frac{(b Sector - a Sector) \cdot \sin (2 \cdot ∠ Leg(1))}{a Sector + b Sector + ((b Sector - a Sector) \cdot \cos (2 \cdot ∠ Leg(1)))}))

A_Sec - Area of Elliptical Sector?a_Sector - Semi Major Axis of Elliptical Sector?b_Sector - Semi Minor Axis of Elliptical Sector?∠_Sector - Angle of Elliptical Sector?∠_Leg(2) - Second Leg Angle of Elliptical Sector?∠_Leg(1) - First Leg Angle of Elliptical Sector?

Area of Elliptical Sector Example

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

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

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

34.1432 = (\frac{10 \cdot 6}{2}) \cdot (90 - a \tan (\frac{(6 - 10) \cdot \sin (2 \cdot 120)}{10 + 6 + ((6 - 10) \cdot \cos (2 \cdot 120))}) + a \tan (\frac{(6 - 10) \cdot \sin (2 \cdot 30)}{10 + 6 + ((6 - 10) \cdot \cos (2 \cdot 30))}))

34.1432m² = (\frac{10m \cdot 6m}{2}) \cdot (90° - a \tan (\frac{(6m - 10m) \cdot \sin (2 \cdot 120°)}{10m + 6m + ((6m - 10m) \cdot \cos (2 \cdot 120°))}) + a \tan (\frac{(6m - 10m) \cdot \sin (2 \cdot 30°)}{10m + 6m + ((6m - 10m) \cdot \cos (2 \cdot 30°))}))

34.1432 = (\frac{10 \cdot 6}{2}) \cdot (90 - a \tan (\frac{(6 - 10) \cdot \sin (2 \cdot 120)}{10 + 6 + ((6 - 10) \cdot \cos (2 \cdot 120))}) + a \tan (\frac{(6 - 10) \cdot \sin (2 \cdot 30)}{10 + 6 + ((6 - 10) \cdot \cos (2 \cdot 30))}))

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Area of Elliptical Sector Solution

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

FIRST Step Consider the formula

A Sec = (\frac{a Sector \cdot b Sector}{2}) \cdot (∠ Sector - a \tan (\frac{(b Sector - a Sector) \cdot \sin (2 \cdot ∠ Leg(2))}{a Sector + b Sector + ((b Sector - a Sector) \cdot \cos (2 \cdot ∠ Leg(2)))}) + a \tan (\frac{(b Sector - a Sector) \cdot \sin (2 \cdot ∠ Leg(1))}{a Sector + b Sector + ((b Sector - a Sector) \cdot \cos (2 \cdot ∠ Leg(1)))}))

Next Step Substitute values of Variables

∴

A Sec = (\frac{10m \cdot 6m}{2}) \cdot (90° - a \tan (\frac{(6m - 10m) \cdot \sin (2 \cdot 120°)}{10m + 6m + ((6m - 10m) \cdot \cos (2 \cdot 120°))}) + a \tan (\frac{(6m - 10m) \cdot \sin (2 \cdot 30°)}{10m + 6m + ((6m - 10m) \cdot \cos (2 \cdot 30°))}))

Next Step Convert Units

∴

A Sec = (\frac{10m \cdot 6m}{2}) \cdot (1.5708rad - a \tan (\frac{(6m - 10m) \cdot \sin (2 \cdot 2.0944rad)}{10m + 6m + ((6m - 10m) \cdot \cos (2 \cdot 2.0944rad))}) + a \tan (\frac{(6m - 10m) \cdot \sin (2 \cdot 0.5236rad)}{10m + 6m + ((6m - 10m) \cdot \cos (2 \cdot 0.5236rad))}))

Next Step Prepare to Evaluate

∴

A Sec = (\frac{10 \cdot 6}{2}) \cdot (1.5708 - a \tan (\frac{(6 - 10) \cdot \sin (2 \cdot 2.0944)}{10 + 6 + ((6 - 10) \cdot \cos (2 \cdot 2.0944))}) + a \tan (\frac{(6 - 10) \cdot \sin (2 \cdot 0.5236)}{10 + 6 + ((6 - 10) \cdot \cos (2 \cdot 0.5236))}))

Next Step Evaluate

∴

A Sec = 34.1432054805833m²

LAST Step Rounding Answer

∴

A Sec = 34.1432m²

Area of Elliptical Sector Formula Elements

Variables

Functions

Area of Elliptical Sector

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

Symbol: A_Sec

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Elliptical Sector

Semi Major Axis of Elliptical Sector

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

Symbol: a_Sector

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Semi Major Axis of Elliptical Sector

Semi Minor Axis of Elliptical Sector

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

Symbol: b_Sector

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Semi Minor Axis of Elliptical Sector

Angle of Elliptical Sector

Angle of Elliptical Sector is the angle made by the linear edges of the sector at the center of the Elliptical Sector.

Symbol: ∠_Sector

Measurement: AngleUnit: °

Note: Value should be between 0 to 180.

Formulas to find Angle of Elliptical Sector

Second Leg Angle of Elliptical Sector

Second Leg Angle of Elliptical Sector is the angle made by the semi major axis on the right and the linear edge of the sector which is far from that semi major axis of the Elliptical Sector.

Symbol: ∠_Leg(2)

Measurement: AngleUnit: °

Note: Value should be between 0 to 180.

Formulas to find Second Leg Angle of Elliptical Sector

First Leg Angle of Elliptical Sector

First Leg Angle of Elliptical Sector is the angle made by the semi major axis on the right and the linear edge of the sector which is adjacent to that semi major axis of the Elliptical Sector.

Symbol: ∠_Leg(1)

Measurement: AngleUnit: °

Note: Value should be between 0 to 180.

Formulas to find First Leg Angle of Elliptical Sector

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

cos

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

Syntax: cos(Angle)

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

atan

Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle.

Syntax: atan(Number)

Other formulas in Elliptical Sector category

Go Angle of Elliptical Sector

∠ Sector = ∠ Leg(2) - ∠ Leg(1)

Go First Leg Angle of Elliptical Sector

∠ Leg(1) = ∠ Leg(2) - ∠ Sector

Go Second Leg Angle of Elliptical Sector

∠ Leg(2) = ∠ Sector + ∠ Leg(1)

Go First Leg of Elliptical Sector

l 1 = \sqrt{\frac{{a Sector}^{2} \cdot {b Sector}^{2}}{({a Sector}^{2} \cdot {\sin (∠ Leg(1))}^{2}) + ({b Sector}^{2} \cdot {\cos (∠ Leg(1))}^{2})}}

How to Evaluate Area of Elliptical Sector?

Area of Elliptical Sector evaluator uses Area of Elliptical Sector = ((Semi Major Axis of Elliptical Sector*Semi Minor Axis of Elliptical Sector)/2)*(Angle of Elliptical Sector-atan(((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*sin(2*Second Leg Angle of Elliptical Sector))/(Semi Major Axis of Elliptical Sector+Semi Minor Axis of Elliptical Sector+((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*cos(2*Second Leg Angle of Elliptical Sector))))+atan(((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*sin(2*First Leg Angle of Elliptical Sector))/(Semi Major Axis of Elliptical Sector+Semi Minor Axis of Elliptical Sector+((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*cos(2*First Leg Angle of Elliptical Sector))))) to evaluate the Area of Elliptical Sector, Area of Elliptical Sector formula is defined as the total quantity of plane enclosed by the boundary of the Elliptical Sector. Area of Elliptical Sector is denoted by A_Sec symbol.

How to evaluate Area of Elliptical Sector using this online evaluator? To use this online evaluator for Area of Elliptical Sector, enter Semi Major Axis of Elliptical Sector (a_Sector), Semi Minor Axis of Elliptical Sector (b_Sector), Angle of Elliptical Sector (∠_Sector), Second Leg Angle of Elliptical Sector (∠_Leg(2)) & First Leg Angle of Elliptical Sector (∠_Leg(1)) and hit the calculate button.

FAQs on Area of Elliptical Sector

What is the formula to find Area of Elliptical Sector?

The formula of Area of Elliptical Sector is expressed as Area of Elliptical Sector = ((Semi Major Axis of Elliptical Sector*Semi Minor Axis of Elliptical Sector)/2)*(Angle of Elliptical Sector-atan(((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*sin(2*Second Leg Angle of Elliptical Sector))/(Semi Major Axis of Elliptical Sector+Semi Minor Axis of Elliptical Sector+((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*cos(2*Second Leg Angle of Elliptical Sector))))+atan(((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*sin(2*First Leg Angle of Elliptical Sector))/(Semi Major Axis of Elliptical Sector+Semi Minor Axis of Elliptical Sector+((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*cos(2*First Leg Angle of Elliptical Sector))))). Here is an example- 34.14321 = ((10*6)/2)*(1.5707963267946-atan(((6-10)*sin(2*2.0943951023928))/(10+6+((6-10)*cos(2*2.0943951023928))))+atan(((6-10)*sin(2*0.5235987755982))/(10+6+((6-10)*cos(2*0.5235987755982))))).

How to calculate Area of Elliptical Sector?

With Semi Major Axis of Elliptical Sector (a_Sector), Semi Minor Axis of Elliptical Sector (b_Sector), Angle of Elliptical Sector (∠_Sector), Second Leg Angle of Elliptical Sector (∠_Leg(2)) & First Leg Angle of Elliptical Sector (∠_Leg(1)) we can find Area of Elliptical Sector using the formula - Area of Elliptical Sector = ((Semi Major Axis of Elliptical Sector*Semi Minor Axis of Elliptical Sector)/2)*(Angle of Elliptical Sector-atan(((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*sin(2*Second Leg Angle of Elliptical Sector))/(Semi Major Axis of Elliptical Sector+Semi Minor Axis of Elliptical Sector+((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*cos(2*Second Leg Angle of Elliptical Sector))))+atan(((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*sin(2*First Leg Angle of Elliptical Sector))/(Semi Major Axis of Elliptical Sector+Semi Minor Axis of Elliptical Sector+((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*cos(2*First Leg Angle of Elliptical Sector))))). This formula also uses Sine (sin)Cosine (cos)Tangent (tan), Inverse Tan (atan) function(s).

Can the Area of Elliptical Sector be negative?

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

Which unit is used to measure Area of Elliptical Sector?

Area of Elliptical Sector 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 Sector can be measured.

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Area of Elliptical Sector Formula

Area of Elliptical Sector Example

Area of Elliptical Sector Solution

Area of Elliptical Sector Formula Elements

Other formulas in Elliptical Sector category

How to Evaluate Area of Elliptical Sector?

FAQs on Area of Elliptical Sector

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