Question

the figure below is made of a square and half - circles. find the total area of the figure. area of one half circle =

Explanation:

Step1: Calculate area of square

The side - length of the square is $20$ ft. The area of a square $A_{square}=s^2$, where $s = 20$ ft. So $A_{square}=20^2=400$ square feet.

Step2: Calculate area of one semi - circle

The diameter of each semi - circle is $20$ ft, so the radius $r = 10$ ft. The area of a full - circle is $A=\pi r^2$, and the area of a semi - circle $A_{semicircle}=\frac{1}{2}\pi r^2$. Substituting $r = 10$ ft, we get $A_{semicircle}=\frac{1}{2}\pi\times10^2 = 50\pi$ square feet.

Step3: Calculate total area of two semi - circles

Since there are two semi - circles of the same size, the combined area of the two semi - circles $A_{circles}=2\times\frac{1}{2}\pi r^2=\pi r^2$. With $r = 10$ ft, $A_{circles}=100\pi$ square feet.

Step4: Calculate total area of the figure

The total area of the figure $A = A_{square}+A_{circles}$. Substituting the values of $A_{square}$ and $A_{circles}$, we get $A=400 + 100\pi$ square feet.

Answer:

$400+100\pi$ square feet