To find the area of the figure, we will calculate the areas of the rectangle and the two triangles separately and then combine them.
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Area of the Rectangle: The formula for the area of a rectangle is: \[ A = B \times H \] where \( B \) is the base and \( H \) is the height.
For the rectangle:
- Base \( B = 8 , \text{in} \)
- Height \( H = 2 , \text{in} \)
So, the area of the rectangle is: \[ A_{\text{rectangle}} = 8 , \text{in} \times 2 , \text{in} = 16 , \text{in}^2 \]
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Area of Triangle 1: The formula for the area of a triangle is: \[ A = \frac{B \times H}{2} \] where \( B \) is the base and \( H \) is the height.
For Triangle 1:
- Base \( B = 5 , \text{in} \)
- Height \( H = 3 , \text{in} \)
So, the area of Triangle 1 is: \[ A_{\text{triangle1}} = \frac{5 , \text{in} \times 3 , \text{in}}{2} = \frac{15 , \text{in}^2}{2} = 7.5 , \text{in}^2 \]
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Area of Triangle 2: Triangle 2 has the same dimensions as Triangle 1 (5 in and 3 in).
So, the area of Triangle 2 is also: \[ A_{\text{triangle2}} = \frac{5 , \text{in} \times 3 , \text{in}}{2} = \frac{15 , \text{in}^2}{2} = 7.5 , \text{in}^2 \]
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Total Area: Now, we combine all the areas: \[ A_{\text{total}} = A_{\text{rectangle}} + A_{\text{triangle1}} + A_{\text{triangle2}} \] \[ A_{\text{total}} = 16 , \text{in}^2 + 7.5 , \text{in}^2 + 7.5 , \text{in}^2 \] \[ A_{\text{total}} = 16 , \text{in}^2 + 15 , \text{in}^2 \] \[ A_{\text{total}} = 31 , \text{in}^2 \]
Thus, the total area of the figure is: \[ \boxed{31 , \text{in}^2} \]