Final answer:
To find the area of the shape, calculate the area of the half-circle and the square separately, then add them together. The area of the half-circle is found using the formula A = (πr^2)/2, and the area of the square is found by multiplying the length of one of its sides by itself. Finally, add the two areas together to get the total area.
Step-by-step explanation:
The shape described consists of a half-circle attached to a square. To find the area, we need to calculate the area of the half-circle and the area of the square separately, then add them together. First, let's find the area of the half-circle using the formula A = (πr^2)/2, where r is the radius of the half-circle. In this case, the radius is half the length of the side of the square, which is 21/2 inches. Substituting the value into the formula, we get A = (3.14) * ((21/2)/2)^2/2 = (3.14) * (21/4)^2/2.
Next, let's find the area of the square. The area of a square is calculated by multiplying the length of one of its sides by itself. In this case, the side length is 21 inches, so the area of the square is 21 * 21 = 441 square inches.
Now, we can add the area of the half-circle to the area of the square to get the total area of the shape. A = (3.14) * (21/4)^2/2 + 441 = 550.5875 square inches. Rounding to the nearest whole number, the area is approximately 551 square inches.