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Answer:

The length of AB is;


12\text{ ft}

Step-by-step explanation:

Given the isosceles trapezoid in the attached image.

The length of line segment AE will be;


\begin{gathered} AE=(28-12)/(2)=(16)/(2) \\ AE=8\text{ ft} \end{gathered}

We can then use the Pythagorean theorem to solve for the length of the line segment AB;


\begin{gathered} AB^2=AE^2+BE^2 \\ AB^2=8^2+9^2 \\ AB^2=64+81 \\ AB=\sqrt[]{64+81} \\ AB=\sqrt[]{145} \\ AB=12.04ft \\ AB=12\text{ ft} \end{gathered}

Therefore, the length of AB is;


12\text{ ft}

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