Melissa is making a piece for a stained glass window that has the shape and measures shown below. Point C is the center of the partial circle that forms one corner of the stained glass piece.
Which area is the closest to the area of the stained glass piece in square inches? Use 3.14 for
269.04
280.26
184.26
148.26
184.26
Shape not shown.
To find the area of the stained glass piece, we need to determine the area of the partial circle and the rectangle. Let's break it down step by step:
1. Find the area of the partial circle:
- The radius of the partial circle is AC.
- The formula for the area of a circle is A = πr^2, where π is approximately 3.14 and r is the radius.
- In this case, the radius is the length of AC, which is 7 inches.
- Calculating the area of the partial circle: A = 3.14 * 7^2 = 3.14 * 49 = 153.86 square inches (approximately).
2. Find the area of the rectangle:
- The length of the rectangle is CD, which is 12 inches.
- The width of the rectangle is AB, which is the diameter of the partial circle and thus 14 inches.
- The formula for the area of a rectangle is A = length * width.
- Calculating the area of the rectangle: A = 12 * 14 = 168 square inches.
3. Add the areas of the partial circle and the rectangle:
- Total area of the stained glass piece = area of the partial circle + area of the rectangle.
- Calculating the total area: 153.86 + 168 = 321.86 square inches (approximately).
Now, let's compare this to the options provided:
269.04 - This option is larger than the calculated area of 321.86 square inches.
280.26 - This option is larger than the calculated area of 321.86 square inches.
184.26 - This option is smaller than the calculated area of 321.86 square inches.
148.26 - This option is smaller than the calculated area of 321.86 square inches.
Therefore, the closest area to the stained glass piece is 321.86 square inches, which is not among the given options.