Valentine is around the corner

Counting squares and half-squares gives approx. 24 square units. Using math, divide the 6 by 6 square into 4 quadrants. The 2 bottom quadrants are 3 by 3 with the heart using up approx. half of the quadrant so the area of each quadrant is approx. $3\times 3 \div 2 \approx4.5$ . Thus the area of the bottom half is $\approx9$ . Then cut the top 2 quadrants into two halves horizontally with a line at 4.5, giving a 6 by 1.5 rectangle and two half circles with radius $\approx1.4$ covered by the heart. Area of top half is approx. $6\times 1.5 + \pi(1.4)^2\approx15$ . The total area is bottom plus top: $9+15\approx\boxed{24}$