1 Answer

JMoura · Answer 1 · 2023-05-27T19:20:42+0000

We have a rectangular room with a length of 16 feet and a width of 14 ft, and a circular rug inside the room with a radius of 4.5 feet.

The following diagram represents the situation:

What we need to find is the red area.

The first step will be to calculate the area of the rectangle:

$A_{\text{rectangle}}=l* w$

where l is the length l=16ft and w is the width w=14ft. We substitute l and w and find the area of the complete rectangle:

$\begin{gathered} A_{\text{rectangle}}=16ft*14ft \\ A_{\text{rectangle}}=224ft^2 \end{gathered}$

The second step is to calculate the area of the circle:

$A_{\text{circle}}=\pi r^2$

Where π=3.1416 and r is the radius, r=4.5 ft. Substituting those values, we can find the area of the circle:

$A_{\text{circle}}=(3.1416)(4.5ft)^2$

Solving the operations:

$\begin{gathered} A_{\text{circle}}=(3.1416)(20.25ft^2) \\ A_{\text{circle}}=63.617ft^2 \end{gathered}$

The third step is to subtract the area of the circle to the area of the rectangle in order to find the amount of floor left uncovered:

$A_{\text{uncovered}}=A_{\text{rectangle}}-A_{\text{circle}}$

Substituting the known areas:

$\begin{gathered} A_{\text{uncovered}}=224ft^2-63.617ft^2 \\ A_{\text{uncovered}}=160.383ft^2 \end{gathered}$

Answer:

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