DAY 30

Comment

One approach is to count squares and fractions of squares, but it is easier to do this for the area outside the triangle than for the area inside the triangle.

Answer

4 square centimetres.

Readers' methods

PR of Stevenage:

The area of A is 1 square cm (half of a rectangle of area 2 sq cm);
the area of B is also 1 square cm;
the area of C is (3 - 1) square cm (half of 6 - half of 2);
1 + 1 + 2 = 4.

Kevin B, Birmingham B13:
Using Pick's theorem for areas based on a lattice, we have
b/2 + c - 1 (where b = points on boundary and c = points within boundary);
substituting gives 4/2 + 3 - 1, which is 4,
so the area is 4 sq cm.