To find the area of the combined shape, we need to calculate the area of the triangle and the area of the rectangle separately and then add them together.
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Rectangle: The area of a rectangle is given by the formula: \[ \text{Area}_{\text{rectangle}} = \text{width} \times \text{height} \] Assuming the rectangle is the top part of the shape and is 12 feet wide, let's say it is also 8 feet tall (this is an example; you can adjust the height according to your needs).
\[ \text{Area}_{\text{rectangle}} = 12 , \text{ft} \times 8 , \text{ft} = 96 , \text{ft}^2 \]
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Triangle: The area of a triangle is given by the formula: \[ \text{Area}{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} \] For this triangle, the base is also 12 feet wide, and let's say the height of the triangle is the remaining height from the total height of 20 feet after accounting for the rectangle's height. If the rectangle is 8 feet tall, the height of the triangle would be: \[ \text{Height}{\text{triangle}} = 20 , \text{ft} - 8 , \text{ft} = 12 , \text{ft} \]
Therefore, \[ \text{Area}_{\text{triangle}} = \frac{1}{2} \times 12 , \text{ft} \times 12 , \text{ft} = \frac{1}{2} \times 144 , \text{ft}^2 = 72 , \text{ft}^2 \]
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Total Area: Now add the area of the triangle and the rectangle together: \[ \text{Total Area} = \text{Area}{\text{rectangle}} + \text{Area}{\text{triangle}} = 96 , \text{ft}^2 + 72 , \text{ft}^2 = 168 , \text{ft}^2 \]
So, the combined area of the triangle and rectangle is 168 square feet. If you have different dimensions for the triangle or rectangle, you will need to substitute those values in to recalculate the areas accordingly.