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Math Help - Area

  1. #1
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    Area

    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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  2. #2
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    Quote Originally Posted by sa87uk View Post
    I require some help?

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


    thanks in advance
    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

    The area is calculated by:

    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.
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