Question

the figure below is made of a square and half circles. find the total area of the figure. 16 ft 16 ft area of one half circle = 1/2 π 8² 16² 32² +

Explanation:

Step1: Find radius of half - circle

The diameter of each half - circle is equal to the side of the square, which is 16 ft. So the radius $r=\frac{16}{2}=8$ ft.

Step2: Calculate area of one half - circle

The formula for the area of a full - circle is $A = \pi r^{2}$. The area of a half - circle is $A_{half}=\frac{1}{2}\pi r^{2}$. Substituting $r = 8$ ft, we get $A_{half}=\frac{1}{2}\pi\times8^{2}$.

Step3: Calculate area of the square

The side of the square $s = 16$ ft. The area of the square $A_{square}=s^{2}=16^{2}$ square feet.

Step4: Calculate total area of the figure

The figure is composed of a square and two half - circles (which is equivalent to one full - circle). The total area $A = A_{square}+A_{circle}$. Since $A_{circle}=\pi r^{2}=\pi\times8^{2}$ and $A_{square}=16^{2}$, the total area $A=16^{2}+\pi\times8^{2}$.

Answer:

$16^{2}+\pi\times8^{2}$ square feet