# Plane Areas

## 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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## Example 8 | Area bounded by arcs of quarter circles

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## Example 7 | Area inside the square not common to the quarter circles

**Problem**

The figure shown below is composed of arc of circles with centers at each corner of the square 20 cm by 20 cm. Find the area inside the square but outside the region commonly bounded by the quarter circles. The required area is shaded as shown in the figure below.

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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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## Example 6 | Plane Areas in Rectangular Coordinates

**Example 6**

Find each of the two areas bounded by the curves *y* = *x*^{3} - 4*x* and *y* = *x*^{2} + 2*x*.

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