# Area

• January 13th 2009, 10:40 AM
sa87uk
Area
I require some help?

Calculate the area of a regular fifteen-sided figure inscribed in a circle of radius 10cm???

• January 13th 2009, 10:47 AM
earboth
Quote:

Originally Posted by sa87uk
I require some help?

Calculate the area of a regular fifteen-sided figure inscribed in a circle of radius 10cm???

A regular 15-gon consists of 15 isosceles triangles which can be split into 2 right triangles each. The central angle of one triangle is $\alpha = \dfrac{360^\circ}{15}=24^\circ$
$a=15\cdot \underbrace{r\cdot \sin\left(\frac{24^\circ}2\right)}_{half\ base} \cdot \underbrace{r \cdot \cos \left(\frac{24^\circ}2\right)}_{height\ of\ triangle} = 15 \cdot r^2 \cdot \sin(12^\circ) \cdot \cos(12^\circ)$