The area of a sector is the portion of a circle enclosed by two radii and an arc. It is a useful concept in fields such as geometry, physics, and engineering. For example, in civil engineering, the area of a sector can be used to calculate the amount of land needed for a circular parking lot or a roundabout. In physics, the area of a sector can be used to calculate the amount of solar energy received by a solar panel, which is proportional to the area of the panel facing the sun. Additionally, the area of a sector is used in various calculations involving circles and angles.

The formula for determining the area of an elliptical sector is defined as:

\(A\) \(=\) \(\int_{\theta_1}^{\theta_2} \dfrac{a^2 \cdot b^2}{2 \cdot (b^2 \cdot cos^2(\theta) + a^2 \cdot sin^2(\theta))}d\theta\)

\(A\): the area of the sector

\(\theta_1\): The angle of between the a axis and the first leg of the sector.

\(\theta_2\): The angle of between the a axis and the second leg of the sector.

\(a\): the length of axis a

\(b\): the length of the axis b

The SI unit of area is: \(square \text{ } meter\text{ }(m^2)\)

## Find \(A\)

Use this calculator to determine the area of an elliptical sector using the lengths of the axes and the angles.

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The angle of between the a axis and the first leg of the sector.

\(\theta_1\)

\(degree\)

The angle of between the a axis and the second leg of the sector.

\(\theta_2\)

\(degree\)

the length of axis a

\(a\)

\(meter\)

the length of the axis b

\(b\)

\(meter\)

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