# How do you find the area ( if any ) common to the four cardioids #r=1+-cos theta and r = 1+-sin theta#?

##### 1 Answer

#### Explanation:

The lines of symmetry (axes ) of the cardioids are the positive and

negative axes of coordinates.

The cardioids are equal in size and symmetrically placed, with

respect to the pole r=0 that is a common point of imtersection for all.

The common area comprises four equal parts.

The other terminal points, in these parts, are

Now, one such part is the area in

symmetrical about

This area =

r from 0 to

After integration with respect to r, this becomes

The total common area is 4 X this area

I welcome a graphical depiction for my answer..

.

,