To find the total area of the porch, we can divide it into two parts: the wooden part (which is a right triangle) and the concrete part (which is a square).
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Area of the right triangle (wooden part):
- The formula for the area of a right triangle is: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
- Here, we can use \( a = 21 \) ft as the base and \( b = 28 \) ft as the height.
- Therefore, the area of the wooden part is: \[ \text{Area}_{\text{triangle}} = \frac{1}{2} \times 21 , \text{ft} \times 28 , \text{ft} \] \[ = \frac{1}{2} \times 588 , \text{ft}^2 = 294 , \text{ft}^2 \]
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Area of the square (concrete part):
- The formula for the area of a square is: \[ \text{Area} = \text{side}^2 \]
- Since it is mentioned that the side of the square is \( c = 35 \) ft, the area of the square part is: \[ \text{Area}_{\text{square}} = 35 , \text{ft} \times 35 , \text{ft} = 1225 , \text{ft}^2 \]
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Total area of the porch:
- Now, we add the areas of both parts: \[ \text{Total Area} = \text{Area}{\text{triangle}} + \text{Area}{\text{square}} = 294 , \text{ft}^2 + 1225 , \text{ft}^2 \] \[ = 1519 , \text{ft}^2 \]
Thus, the total area of the porch is 1519 square feet.