Answer:
[tex]A=\frac{3\sqrt{55}}{2}[/tex]
Step-by-step explanation:
For a height h, a perimeter P, and an area A, use the following formula:
[tex]A=\frac{1}{4}h\sqrt{P^{2}-4h^{2} }[/tex]
Next, replace the variables with the given values:
[tex]A=\frac{1}{4}(3)\sqrt{(16)^{2}-4(3)^{2} }[/tex]
Solve the inside of the square root:
[tex]A=\frac{1}{4}(3)\sqrt{256-36}\\A=\frac{1}{4}(3)\sqrt{220}[/tex]
Multiply outside of the square root:
[tex]A=\frac{3}{4}\sqrt{220}\\[/tex]
Simplify the square root:
[tex]A=(\frac{3}{4})2\sqrt{55}\\[/tex]
Multiply outside of the square root once more:
[tex]A=\frac{3}{2}\sqrt{55}\\[/tex]
Simplify:
[tex]A=\frac{3\sqrt{55}}{2}[/tex], or ≈ 11.12429773
