Question

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a circle is drawn within a square as shown.
what is the best approximation for the area of
the shaded region?
use 3.14 to approximate pi.
168.56 in²
696.08 in²
740.04 in²
1677.76 in²
28 in

Explanation:

Step1: Calculate square area

The side length of the square is equal to the diameter of the circle, which is 28 in. The area of a square is side length squared.
$A_{square} = 28^2 = 784 \text{ in}^2$

Step2: Calculate circle radius

The radius of the circle is half the diameter.
$r = \frac{28}{2} = 14 \text{ in}$

Step3: Calculate circle area

Use the formula for the area of a circle $A_{circle} = \pi r^2$, with $\pi=3.14$.
$A_{circle} = 3.14 \times 14^2 = 3.14 \times 196 = 615.44 \text{ in}^2$

Step4: Find shaded area

Subtract the circle area from the square area.
$A_{shaded} = 784 - 615.44$

Answer:

168.56 in² (Option A)