Question

1. denise is planning to put a deck in her back yard. the deck will be a 20 - ft by 12 - ft rectangle with a semicircle of diameter 6 feet, as shown below. find the area of the deck.

Explanation:

Step1: Calculate rectangle area

The area formula for a rectangle is $A = l\times w$. Here, $l = 20$ ft and $w = 12$ ft. So $A_{rectangle}=20\times12 = 240$ square - feet.

Step2: Calculate semi - circle area

The area formula for a full - circle is $A=\pi r^{2}$, and for a semi - circle it's $A_{semicircle}=\frac{1}{2}\pi r^{2}$. Given diameter $d = 6$ feet, then radius $r=\frac{d}{2}=3$ feet. So $A_{semicircle}=\frac{1}{2}\pi\times3^{2}=\frac{9\pi}{2}\approx\frac{9\times3.14}{2}=14.13$ square - feet.

Step3: Calculate total deck area

The total area of the deck $A = A_{rectangle}+A_{semicircle}$. So $A=240 + 14.13=254.13$ square feet.

Answer:

$254.13$ square feet