Final answer:
To calculate the area of Spencer's 7x7 quilt, each square patch measuring 1 3/4 inches is calculated for area (3.0625 sq. in.) and then multiplied by the total number of patches (49), resulting in a total quilt area of 150.0625 square inches.
Step-by-step explanation:
Spencer made a quilt for his cousin's doll with a 7x7 array of square patches. To find the area of the whole quilt, we need to calculate the area of one patch and then multiply by the total number of patches. The length of each patch is 1 3/4 inches, which can also be represented as 1.75 inches.
First, we find the area of one patch:
- Area of one patch = side length × side length
- Area of one patch = 1.75 inches × 1.75 inches
- Area of one patch = 3.0625 square inches
Since there are 49 patches in total (7 patches per row × 7 rows), we then find the total area:
- Total area = area of one patch × total number of patches
- Total area = 3.0625 square inches × 49
- Total area = 150.0625 square inches
Therefore, the area of Spencer's quilt is 150.0625 square inches.