# Polar Area

## 03 Area Enclosed by Cardioids: r = a(1 + sin θ); r = a(1 - sin θ), r = a(1 + cos θ), r = a(1 - cos θ)

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## 08 Area Enclosed by r = a sin 3θ and r = a cos 3θ

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## 05 Area Enclosed by r = a sin 2θ and r = a cos 2θ

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## 01 Area Enclosed by r = 2a cos^2 θ

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## 07 Area Enclosed by r = 2a cos θ and r = 2a sin θ

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## Area for grazing by the goat tied to a silo

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## 06 Area Within the Curve r^2 = 16 cos θ

**Example 6**

What is the area within the curve r^{2} = 16 cos θ?

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## 05 Area Enclosed by Four-Leaved Rose r = a cos 2θ

Find the area enclosed by four-leaved rose r = a cos 2θ.

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## 04 Area of the Inner Loop of the Limacon r = a(1 + 2 cos θ)

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## 03 Area Inside the Cardioid r = a(1 + cos θ) but Outside the Circle r = a

**Example 3**

Find the area inside the cardioid *r* = *a*(1 + cos θ) but outside the circle *r* = *a*.

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