Answer:
[tex]Height=\boxed{10\sqrt{2}} [/tex]
[tex] Area =\boxed{165\sqrt{2}} [/tex]
Step-by-step explanation:
By geometric mean theorem:
[tex] AC=\sqrt{25\times 8}[/tex]
[tex] AC=\sqrt{5^2 \times 2^2 \times 2}[/tex]
[tex] AC=5\times 2\sqrt{2}[/tex]
[tex] AC=10\sqrt{2}[/tex]
So,
[tex]Height=\boxed{10\sqrt{2}} [/tex]
[tex] Area = \frac{1}{2} \times base\times height [/tex]
[tex] \therefore Area = \frac{1}{2} \times (25+8)\times 10\sqrt{2} [/tex]
[tex] \therefore Area =33\times 5\sqrt{2} [/tex]
[tex] Area =\boxed{165\sqrt{2}} [/tex]
