What percentage of the square is Red?

We have $25$ congruent squares, $16$ of them are half white.

The part that is red is $9$ red squares and $16$ half-red squares.

The percentage of red area is $9+\frac{16}{2} \text {out of } 25 = \frac{17}{25} = 0.68 = 68\%$

We can solve this problem by similarity concept.Let the side of the little squares is a. Then the side of the big square is (4√2 a + 2a/√2) = 5a√2. So the area ratio of the big square to white square = 50. The red region has area of 50a^2 – 16 a^2 = 34 a^2 .So the percentage of the square is red = 34 a^2 /(50a^2) . 100% = 68%.