I require some help?

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

thanks in advance

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- Jan 13th 2009, 10:40 AMsa87ukArea
*I require some help?*

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

thanks in advance

- Jan 13th 2009, 10:47 AMearboth
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 $\displaystyle \alpha = \dfrac{360^\circ}{15}=24^\circ$

The area is calculated by:

$\displaystyle a=15\cdot \underbrace{r\cdot \sin\left(\frac{24^\circ}2\right)}_{half\ base} \cdot \underbrace{r \cdot \cos \left(\frac{24^\circ}2\right)}_{height\ of\ triangle} = 15 \cdot r^2 \cdot \sin(12^\circ) \cdot \cos(12^\circ)$

Plug in r = 10 and calculate the value.