To find the total area of the shape described, which consists of a square and two semicircles, we can break it down into parts.
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Area of the Square: The side length of the square is 2 inches. \[ \text{Area of the square} = \text{side}^2 = 2^2 = 4 , \text{in}^2 \]
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Area of the Semicircles: The diameter of each semicircle is also 2 inches, meaning the radius is: \[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{2}{2} = 1 , \text{in} \] The area of a full circle is given by the formula \( \pi r^2 \). Since we have a semicircle, we will take half of that: \[ \text{Area of one semicircle} = \frac{\pi r^2}{2} = \frac{3.14 \times 1^2}{2} = \frac{3.14}{2} = 1.57 , \text{in}^2 \] Since there are two semicircles: \[ \text{Total area of the semicircles} = 2 \times 1.57 = 3.14 , \text{in}^2 \]
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Total Area of the Shape: Combining the area of the square and the two semicircles: \[ \text{Total area} = \text{Area of the square} + \text{Total area of the semicircles} = 4 + 3.14 = 7.14 , \text{in}^2 \]
Thus, the total area of the shape is 7.14 in².
The correct response is:
- 7.14 in.²
1 answer