1. Given data

   Area of one square = $5.29\,\text{cm}^2$

   Number of squares = $7$

2. Find total area

   $\text{Total area} = 7 \times 5.29 = 37.03\,\text{cm}^2$

3. Apply significant figures rule

   In multiplication, the result should have the same number of significant figures as the factor with the least number of significant figures.

   • $5.29$ has 3 significant figures.
   • $7$ is a counted number (exact number of squares), so it does not limit significant figures.

   Therefore, the answer should be reported with 3 significant figures.

4. Round the result

   $37.03 \to 37.0$

   since $37.0$ has 3 significant figures.

5. Check options

   • A: $37.0\,\text{cm}^2$ ✅
   • B: $37\,\text{cm}^2$ has only 2 significant figures ❌
   • C: $37.030\,\text{cm}^2$ has too many significant figures ❌
   • D: $37.03\,\text{cm}^2$ has too many significant figures ❌

Hence, the correct answer is A.