To find the area of the figure, we will calculate the area of the rectangle and the area of the triangle separately, and then sum them.
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Area of the Rectangle:
- The formula for the area of a rectangle is: \[ \text{Area} = \text{length} \times \text{width} \]
- Given dimensions for the rectangle:
- Length = 8 cm (top side)
- Width = 4 cm (height)
Therefore, the area of the rectangle is: \[ \text{Area}_{\text{rectangle}} = 8 , \text{cm} \times 4 , \text{cm} = 32 , \text{cm}^2 \]
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Area of the Triangle:
- The formula for the area of a triangle is: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
- For the triangle, we need to identify its base and height. Based on your description, since we do not have the height of the triangle, let's consider the right triangle formed by the remaining dimensions.
Assuming the height of the triangle is equal to the height of the rectangle (4 cm), and its base is the additional length when the rectangle extends into a triangle:
- Base of the triangle = Bottom dimension = 10 cm
- Height of triangle = Height of rectangle = 4 cm
Therefore, the area of the triangle is: \[ \text{Area}_{\text{triangle}} = \frac{1}{2} \times 10 , \text{cm} \times 4 , \text{cm} = 20 , \text{cm}^2 \]
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Total Area of the Figure: Finally, to get the total area of the figure, sum the areas of the rectangle and the triangle: \[ \text{Total Area} = \text{Area}{\text{rectangle}} + \text{Area}{\text{triangle}} = 32 , \text{cm}^2 + 20 , \text{cm}^2 = 52 , \text{cm}^2 \]
So, the area of the figure is: \[ \boxed{52} , \text{cm}^2 \]