Final answer:
To determine what percentage of the US flag is taken up by the union, calculate the area of the flag and the union. The flag's area is 190 ft², and the union approximately takes up 41 ft², which is about 21.6% of the flag's area; the closest answer choice is b. 21.2%.
Step-by-step explanation:
To find what percentage of the US flag is taken up by the union, we first calculate the area of the flag and the union and then use these areas to determine the percentage.
The area of the flag is 19 ft × 10 ft = 190 ft2.
The area of the union is 7 5/8 ft × 5 3/8 ft. To calculate this, convert the mixed numbers to improper fractions: (7 × 8 + 5)/8 = 61/8 ft and (5 × 8 + 3)/8 = 43/8 ft. So, the area of the union is (61/8) ft × (43/8) ft = 2623/64 ft2.
To convert 2623/64 ft2 to square feet, divide 2623 by 64, which is approximately 41 ft2.
To find the percentage of the flag's area taken up by the union, divide the union's area by the flag's area and multiply by 100: (41 / 190) × 100 = 21.6%. This means that approximately 21.6 percent of the flag is taken up by the union.
The closest answer provided to 21.6% is option b, which is 21.2%.