Question

the figure below is made of a square and half - circles. find the total area of the figure. area of one half - circle. area of one half circle = 1/2 π 12² + 48² 24² more ↓ enter

Explanation:

Step1: Find radius of half - circle

The diameter of the half - circle is equal to the side of the square, which is 24 ft. So the radius $r=\frac{24}{2}=12$ ft.

Step2: Calculate area of one half - circle

The area of a full - circle is $A = \pi r^{2}$, and the area of a half - circle is $A_{half}=\frac{1}{2}\pi r^{2}$. Substituting $r = 12$ ft, we get $A_{half}=\frac{1}{2}\pi\times12^{2}$.

Step3: Analyze the figure

The figure is composed of 2 half - circles (which is equivalent to 1 full - circle) and 1 square. The side of the square $s = 24$ ft, so the area of the square $A_{square}=24^{2}$. The total area of the figure is the sum of the area of the circle and the area of the square. The area of the circle (from the two half - circles) is $\pi\times12^{2}$ and the area of the square is $24^{2}$.

Answer:

The area of one half - circle is $\frac{1}{2}\pi\times12^{2}$, and the total area of the figure is $\pi\times12^{2}+24^{2}$