Mathematics Notes - Trigonometry Problems and Solutions

The area of a rectangular pentagon is 560 square ft. Find the radii of the circumscribed and inscribed circles.

The area of the regular pentagon can be calculated throught the formula $A_p =5 \frac{1}{2} b~r_i$ and $A_p = 5 \frac{1}{2} \sin 72^o r_{c}^{2} $

$area of a rectangular pentagon is 560 square ft.$

$560 = 5\frac{1}{2} \sin 72^o r_c^2$

$r_c = \sqrt{\frac{560x2}{5\sin 72^o}}$

$r_c = 15.35~ft$

Solve the value of $b$

$\cos 54 = \frac{\frac{b}{2}}{r_c}$

$b = 2(15.35)(\cos 54)$

$b = 18.041 ~ft$

Solve $r_i$

$560 = 5 \frac{1}{2} (18.041)r_i$

$r_i = \frac{560x2}{5x18.041 }$

$r_i = 12.42~ft$