Question

m3|l9 applying area of circles. the figure below is made of a square and half circles. find the total area of the figure. area of one half circle. 28 ft 28 ft area of one half circle = 1/2 π · 28² 14² 56² more ↓

Explanation:

Step1: Determine radius of half - circle

The diameter of the half - circle is equal to the side of the square, which is 28 ft. So the radius $r=\frac{28}{2}=14$ 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 $r = 14$ ft, we get $A_{half}=\frac{1}{2}\pi\times14^{2}$.

Step3: Calculate area of the square

The area of a square with side length $s = 28$ ft is $A_{square}=s^{2}=28^{2}$.

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 $A = A_{square}+A_{circle}=28^{2}+\pi\times14^{2}$.

Answer:

The area of one half - circle is $\frac{1}{2}\pi\times14^{2}$. The total area of the figure is $28^{2}+\pi\times14^{2}$.