Question

find the area of the yellow shaded region. 5 ft area = ? ft² round to the nearest tenth

Explanation:

Step1: Find area of the square

The area formula for a square is $A_{square}=s^2$, where $s = 5$ ft. So $A_{square}=5^2=25$ ft².

Step2: Find area of the circle

The diameter of the circle is equal to the side - length of the square, so $d = 5$ ft and $r=\frac{d}{2}=\frac{5}{2}$ ft. The area formula for a circle is $A_{circle}=\pi r^2$. Substituting $r = \frac{5}{2}$ ft, we get $A_{circle}=\pi(\frac{5}{2})^2=\frac{25\pi}{4}$ ft².

Step3: Find area of the shaded region

The area of the shaded region $A$ is the area of the square minus the area of the circle. So $A = A_{square}-A_{circle}=25-\frac{25\pi}{4}$.

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Answer:

$5.4$ ft²