Help with calc! How would i find the area of an astroid? How would this go for this problem?

Question

find the area of the region enclosed by the astroid x=acos^3 theta,
y=asin^3 theta

Answer 1

1. Convert the parametric equations to Cartesian equations,
by finding sin^2(theta) and cos^2(theta) separately, then add
them together (= 1).
2. Then rearrange the Cartesian equation to : y = f(x).
3. Integrate the function from 0 to a (I think). This should give
you the area of one quarter of the figure.
4. Multiply by 4 to get your final answer.

Answer 2

the area is =3/8*pi*a^2

Answer 3

I got the area A = (5/8)pi*a*a

Please give the detailed steps. if i am wrong.