To find the area given the dimensions of 8 ft, 8 ft, and 5.5 ft, we first need to determine the shape these dimensions represent.
Given these three dimensions, it appears that they form a triangle. To find the area of a triangle when you know all three sides, you can use Heron's formula:
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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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Calculate the area (A) using: \[ A = \sqrt{s(s-a)(s-b)(s-c)} \]
Given the sides:
- \(a = 8\) ft
- \(b = 8\) ft
- \(c = 5.5\) ft
Calculating the semi-perimeter (s): \[ s = \frac{8 + 8 + 5.5}{2} = \frac{21.5}{2} = 10.75 \text{ ft} \]
Now, applying Heron's formula: \[ A = \sqrt{s(s-a)(s-b)(s-c)} \] Substituting the values: \[ A = \sqrt{10.75(10.75 - 8)(10.75 - 8)(10.75 - 5.5)} \] Calculating each term: \[ A = \sqrt{10.75(2.75)(2.75)(5.25)} \] Calculating further: \[ A \approx \sqrt{10.75 \times 2.75 \times 2.75 \times 5.25} \] First, calculate the product inside the square root: \[ 2.75 \times 2.75 = 7.5625 \] Then multiply by \(10.75\) and \(5.25\): \[ 10.75 \times 7.5625 \times 5.25 \approx 429.953125 \] Taking the square root: \[ A \approx \sqrt{429.953125} \approx 20.73 \text{ ft}^2 \]
Thus, the area is approximately: \[ \text{Area} \approx 20.73 \text{ ft}^2 \]