Question

you need to apply tile to a kitchen floor with find the area of the shaded region. round you 1.8 feet 1.7 feet area = ft² question help: message instructor submit question question 12 score on last try: 1 of 1 pts. see details for more. get a similar question

Explanation:

Step1: Find area of rectangle

The formula for the area of a rectangle is \( A_{rectangle} = length \times width \). Here, length is \( 1.8 \) feet and width is \( 1.7 \) feet. So, \( A_{rectangle} = 1.8 \times 1.7 = 3.06 \) square feet.

Step2: Find area of circle

The diameter of the circle is equal to the width of the rectangle, which is \( 1.7 \) feet. So, the radius \( r = \frac{1.7}{2} = 0.85 \) feet. The formula for the area of a circle is \( A_{circle} = \pi r^2 \). Using \( \pi \approx 3.14 \), we get \( A_{circle} = 3.14 \times (0.85)^2 = 3.14 \times 0.7225 = 2.26865 \) square feet.

Step3: Find area of shaded region

The shaded region is the area of the rectangle minus the area of the circle. So, \( A_{shaded} = A_{rectangle} - A_{circle} = 3.06 - 2.26865 = 0.79135 \) square feet. Rounding to a reasonable decimal place (e.g., two decimal places), we get approximately \( 0.79 \) square feet. (If we use a more precise value of \( \pi \), like \( \pi \approx 3.1416 \), \( A_{circle} = 3.1416 \times 0.7225 \approx 2.2698 \), and \( A_{shaded} \approx 3.06 - 2.2698 = 0.7902 \approx 0.79 \) or \( 0.80 \) depending on rounding rules.)

Answer:

\( 0.79 \) (or \( 0.80 \) depending on rounding, but typically \( 0.79 \) when using \( \pi \approx 3.14 \))