2. A. Ineffective Ways to Measure

Area of the Koch curve

We'll try to compute the area of the Koch curve by covering it with isosceles triangles (suggested by the general shape of the Koch curve).

Using smaller and smaller triangles should give a better estimate of the area of the Koch curve.

First, cover the Koch cuve with a single triangle.

This triangle has base length 1 and altitude sqrt(3)/6 (from the Pythagorean theorem),

hence area

A0 = (√3)/12.

Certainly, the area of the Koch curve is less than A0.

Here is the second approximation.

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