An irrational number is any number that cannot be represented by a rational fraction, i.e. a fraction that consists of an integer divided by another integer, e.g. 0.375 = 3/8.

Yes there are an infinite number of irrational numbers, just as DIYSwede said.

If the "oval" Frank mentioned was in reality an ellipse ("oval" is not a recognized name for any geometric figure), the area is given by:

A = pi * a * b

where:

a = length of semi-major axis
b = length of semi-minor axis

Given an ellipse, these lengths are easily found using a compass and ruler.

The teacher was probably going to follow this exercise with the observation that, as the ellipse becomes more and more symmetrical, a and b become equal to a value we'll label 'r', and the area of the resulting circle becomes the familiar...

A = pi * r * r = pi * r^2