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Area of Ellipse given Eccentricity and Semi Minor Axis Formula

GoArea of Ellipse given Major and Minor Axes Formula

GoArea of Ellipse Formula

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

A = \frac{π \cdot b^{2}}{\sqrt{1 - e^{2}}}

A - Area of Ellipse?b - Semi Minor Axis of Ellipse?e - Eccentricity of Ellipse?π - Archimedes' constant?

Area of Ellipse given Eccentricity and Semi Minor Axis Example

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Here is how the Area of Ellipse given Eccentricity and Semi Minor Axis equation looks like with Values.

Here is how the Area of Ellipse given Eccentricity and Semi Minor Axis equation looks like with Units.

Here is how the Area of Ellipse given Eccentricity and Semi Minor Axis equation looks like.

188.4956 = \frac{3.1416 \cdot 6^{2}}{\sqrt{1 - {0.8}^{2}}}

188.4956m² = \frac{3.1416 \cdot {6m}^{2}}{\sqrt{1 - {0.8m}^{2}}}

188.4956 = \frac{3.1416 \cdot 6^{2}}{\sqrt{1 - {0.8}^{2}}}

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Area of Ellipse given Eccentricity and Semi Minor Axis Solution

Follow our step by step solution on how to calculate Area of Ellipse given Eccentricity and Semi Minor Axis?

FIRST Step Consider the formula

A = \frac{π \cdot b^{2}}{\sqrt{1 - e^{2}}}

Next Step Substitute values of Variables

∴

A = \frac{π \cdot {6m}^{2}}{\sqrt{1 - {0.8m}^{2}}}

Next Step Substitute values of Constants

∴

A = \frac{3.1416 \cdot {6m}^{2}}{\sqrt{1 - {0.8m}^{2}}}

Next Step Prepare to Evaluate

∴

A = \frac{3.1416 \cdot 6^{2}}{\sqrt{1 - {0.8}^{2}}}

Next Step Evaluate

∴

A = 188.495559215388m²

LAST Step Rounding Answer

∴

A = 188.4956m²

Area of Ellipse given Eccentricity and Semi Minor Axis Formula Elements

Variables

Constants

Functions

Area of Ellipse

Area of Ellipse is the total quantity of plane enclosed by the boundary of the Ellipse.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Ellipse

Semi Minor Axis of Ellipse

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

Symbol: b

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Semi Minor Axis of Ellipse

Eccentricity of Ellipse

Eccentricity of Ellipse is the ratio of the linear eccentricity to the semi major axis of the Ellipse.

Symbol: e

Measurement: LengthUnit: m

Note: Value should be between 0 to 1.

Formulas to find Eccentricity of Ellipse

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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 to find Area of Ellipse

Go Area of Ellipse given Major and Minor Axes

A = (\frac{π}{4}) \cdot 2a \cdot 2b

Go Area of Ellipse

A = π \cdot a \cdot b

Go Area of Ellipse given Linear Eccentricity and Semi Major Axis

A = π \cdot a \cdot \sqrt{a^{2} - c^{2}}

Go Area of Ellipse given Linear Eccentricity and Semi Minor Axis

A = π \cdot \sqrt{c^{2} + b^{2}} \cdot b

How to Evaluate Area of Ellipse given Eccentricity and Semi Minor Axis?

Area of Ellipse given Eccentricity and Semi Minor Axis evaluator uses Area of Ellipse = (pi*Semi Minor Axis of Ellipse^2)/sqrt(1-Eccentricity of Ellipse^2) to evaluate the Area of Ellipse, The Area of Ellipse given Eccentricity and Semi Minor Axis formula is defined as the total quantity of the plane enclosed by the boundary of the Ellipse, and calculated using the eccentricity and semi-minor axis of the Ellipse. Area of Ellipse is denoted by A symbol.

How to evaluate Area of Ellipse given Eccentricity and Semi Minor Axis using this online evaluator? To use this online evaluator for Area of Ellipse given Eccentricity and Semi Minor Axis, enter Semi Minor Axis of Ellipse (b) & Eccentricity of Ellipse (e) and hit the calculate button.

FAQs on Area of Ellipse given Eccentricity and Semi Minor Axis

What is the formula to find Area of Ellipse given Eccentricity and Semi Minor Axis?

The formula of Area of Ellipse given Eccentricity and Semi Minor Axis is expressed as Area of Ellipse = (pi*Semi Minor Axis of Ellipse^2)/sqrt(1-Eccentricity of Ellipse^2). Here is an example- 188.4956 = (pi*6^2)/sqrt(1-0.8^2).

How to calculate Area of Ellipse given Eccentricity and Semi Minor Axis?

With Semi Minor Axis of Ellipse (b) & Eccentricity of Ellipse (e) we can find Area of Ellipse given Eccentricity and Semi Minor Axis using the formula - Area of Ellipse = (pi*Semi Minor Axis of Ellipse^2)/sqrt(1-Eccentricity of Ellipse^2). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Area of Ellipse?

Here are the different ways to Calculate Area of Ellipse-

Area of Ellipse=(pi/4)*Major Axis of Ellipse*Minor Axis of Ellipse
Area of Ellipse=pi*Semi Major Axis of Ellipse*Semi Minor Axis of Ellipse
Area of Ellipse=pi*Semi Major Axis of Ellipse*sqrt(Semi Major Axis of Ellipse^2-Linear Eccentricity of Ellipse^2)

Can the Area of Ellipse given Eccentricity and Semi Minor Axis be negative?

No, the Area of Ellipse given Eccentricity and Semi Minor Axis, measured in Area cannot be negative.

Which unit is used to measure Area of Ellipse given Eccentricity and Semi Minor Axis?

Area of Ellipse given Eccentricity and Semi Minor Axis 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 Ellipse given Eccentricity and Semi Minor Axis can be measured.

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