geometry formulas for area and perimeter of shapes

Pentagon

circle area and perimeter formula
$$\textbf{Area of the pentagon}$$
$$A = \frac{1}{4} 5 b^2 \cot\bigg(\frac{\pi}{5}\bigg) $$
$$ = \frac{1}{4} 5 b^2 \frac{\cos\big(\frac{\pi}{5}\big)}{\sin\big(\frac{\pi}{5}\big)} $$
$$\textbf{Perimeter of the pentagon}$$
$$P = 5 b $$