Question

find the area to the nearest square foot of the shaded region below, consisting of a square with a circle cut out of it. use 3.14 as an approximation for π.
14 ft
419 square feet
105 square feet
42 square feet
154 square feet

Explanation:

Step1: Find area of square

The side length of the square is equal to the diameter of the circle, which is 14 ft. The area of a square is \( \text{side}^2 \), so \( 14^2 = 196 \) square feet.

Step2: Find area of circle

The radius of the circle is \( \frac{14}{2} = 7 \) ft. The area of a circle is \( \pi r^2 \), using \( \pi = 3.14 \), so \( 3.14 \times 7^2 = 3.14 \times 49 = 153.86 \) square feet.

Step3: Find area of shaded region

Subtract the area of the circle from the area of the square: \( 196 - 153.86 = 42.14 \), which rounds to 42 square feet. Wait, no, wait, I made a mistake. Wait, the square's side is 14, so area is 1414=196? Wait no, wait the diameter of the circle is 14, so the square's side is 14. Then the circle's radius is 7. Area of circle is 3.1477=153.86. Then shaded area is 196 - 153.86 = 42.14, which is approximately 42? But wait, the options have 42. Wait, but let me check again. Wait, maybe I messed up the square's area. Wait, no, 1414 is 196. Circle area is 3.1449=153.86. 196-153.86=42.14, so 42. But wait, the options have 42. But wait, maybe I made a mistake. Wait, no, the problem is a square with a circle cut out. So shaded area is square area minus circle area. So square area: 1414=196. Circle area: 3.14*(7)^2=153.86. 196-153.86=42.14≈42. So the answer is 42 square feet.

Answer:

42 square feet (corresponding to the option "42 square feet")