# Plane Areas

## 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.

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

**Example 6**

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

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

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

## 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*.

## 02 Area Bounded by the Lemniscate of Bernoulli r^2 = a^2 cos 2θ

**Example 2**

Find the area bounded by the lemniscate of Bernoulli r^{2} = a^{2} cos 2θ.