To determine the area based on the provided dimensions, it appears that you may be dealing with a triangular or an irregular shape since you provided three lengths (8 ft, 8 ft, and 5.5 ft). If this is a triangle with sides of lengths 8 ft, 8 ft, and 5.5 ft, we can use Heron's formula to calculate the area.
Here's how Heron's formula works:
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Calculate the semi-perimeter \( s \): \[ s = \frac{a + b + c}{2} \] where \( a \), \( b \), and \( c \) are the lengths of the sides.
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The area \( A \) of the triangle can be calculated using Heron's formula: \[ A = \sqrt{s(s-a)(s-b)(s-c)} \]
Given:
- \( a = 8 \) ft
- \( b = 8 \) ft
- \( c = 5.5 \) ft
Step 1: Calculate the semi-perimeter \( s \): \[ s = \frac{8 + 8 + 5.5}{2} = \frac{21.5}{2} = 10.75 \text{ ft} \]
Step 2: Calculate the area \( A \): \[ A = \sqrt{10.75 \times (10.75 - 8) \times (10.75 - 8) \times (10.75 - 5.5)} \] \[ = \sqrt{10.75 \times 2.75 \times 2.75 \times 5.25} \] \[ = \sqrt{10.75 \times 2.75^2 \times 5.25} \] \[ = \sqrt{10.75 \times 7.5625 \times 5.25} \]
Now, calculating the multiplications step by step:
- \( 2.75^2 = 7.5625 \)
- \( 10.75 \times 7.5625 = 81.1875 \)
- \( 81.1875 \times 5.25 = 426.484375 \)
Now compute the square root: \[ A = \sqrt{426.484375} \approx 20.66 \text{ ft}^2 \]
Thus, the area of the triangle is approximately: \[ A \approx 20.66 \text{ ft}^2 \]
So, the answer is: \[ a \approx 20.66 \text{ ft}^2 \]