To calculate the total area of the composite figure consisting of a square and two semicircles (attached to the left and top), we can break it down step-by-step.
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Area of the Square: The area \( A \) of a square is given by the formula: \[ A = \text{side}^2 \] With the side length of the square being 2 inches: \[ A_{square} = 2^2 = 4 \text{ in}^2 \]
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Area of One Semicircle: The area \( A \) of a circle is given by the formula: \[ A = \pi r^2 \] The diameter of each semicircle is 2 inches, so the radius \( r \) is: \[ r = \frac{2}{2} = 1 \text{ inch} \] Therefore, the area of one semicircle is: \[ A_{semicircle} = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (1)^2 = \frac{1}{2} \pi = \frac{3.14}{2} = 1.57 \text{ in}^2 \]
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Area of Both Semicircles: Since there are two semicircles, we multiply the area of one semicircle by 2: \[ A_{2 , semicircles} = 2 \times 1.57 = 3.14 \text{ in}^2 \]
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Total Area of the Shape: Now, we can combine the areas of the square and the two semicircles: \[ A_{total} = A_{square} + A_{2 , semicircles} = 4 + 3.14 = 7.14 \text{ in}^2 \]
Thus, the total area of the shape is 7.14 in².
So the correct response is: 7.14 in.²
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