Sheila Luk (Year 10, The Mount School, York) saw right through this 'deception' and gave an excellent explanation of the situation.

The cheat is that although each triangle has a side of length 1 cm, the side at right angles to it is of length ¹⁰/ ₁₁ cm. The diagonal of the rectangle does not go through the corners of the squares if it's drawn on squared paper.

The new rectangle, shown dotted, is not 11 by 10, but 10 ¹⁰/ ₁₁ by 10 and the difference in area is exactly ¹⁰/ ₁₁ square cm, the area of the two triangles which were removed.

10 ¹⁰/ ₁₁ x 10 = 109 ¹/ ₁₁= 110 - ¹⁰/ ₁₁