To find the area of the figure composed of the rectangle and the semicircle, we can calculate the areas of each part separately and then add them together.
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Area of the Rectangle: The area \( A \) of a rectangle is given by the formula: \[ A = \text{length} \times \text{height} \] For this rectangle:
- Length = 10 inches
- Height = 4 inches
So, the area of the rectangle is: \[ A_{\text{rectangle}} = 10 , \text{inches} \times 4 , \text{inches} = 40 , \text{inches}^2 \]
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Area of the Semicircle: The area \( A \) of a full circle is given by the formula: \[ A = \pi r^2 \] Since we are dealing with a semicircle, we will take half of the area of the full circle.
The radius \( r \) of the semicircle is half of the height of the rectangle:
- Radius = Height = 4 inches
Now we find the area of the semicircle: \[ A_{\text{semicircle}} = \frac{1}{2} \pi r^2 \] Plugging in the value of \( r \): \[ A_{\text{semicircle}} = \frac{1}{2} \times 3.14 \times (4 , \text{inches})^2 \] \[ = \frac{1}{2} \times 3.14 \times 16 , \text{inches}^2 \] \[ = \frac{1}{2} \times 50.24 , \text{inches}^2 \] \[ = 25.12 , \text{inches}^2 \]
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Total Area of the Figure: Now, we sum the areas of the rectangle and the semicircle: \[ A_{\text{total}} = A_{\text{rectangle}} + A_{\text{semicircle}} = 40 , \text{inches}^2 + 25.12 , \text{inches}^2 \] \[ = 65.12 , \text{inches}^2 \]
Thus, the area of the figure is \( \boxed{65.12} \) square inches.