Question

find the total area of the figure. area of one half - circle =

Explanation:

Step1: Find area of the square

The side - length of the square is 24. The area formula for a square is $A_{square}=s^2$, where $s = 24$. So $A_{square}=24\times24 = 576$.

Step2: Find area of one half - circle

The diameter of the half - circle is 24, so the radius $r=\frac{24}{2}=12$. The area formula for a full - circle is $A=\pi r^2$, and the area of a half - circle is $A_{half - circle}=\frac{1}{2}\pi r^2$. Substituting $r = 12$, we get $A_{half - circle}=\frac{1}{2}\pi\times12^2=\frac{1}{2}\pi\times144 = 72\pi$.

Step3: Find total area of the figure

There are 2 half - circles and 1 square. The total area $A = A_{square}+2\times A_{half - circle}$. Substituting the values we found: $A=576 + 2\times72\pi=576+144\pi$.

Answer:

$576 + 144\pi$