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Thread: Radian Measure: Finding an expression for area

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    Wink Radian Measure: Finding an expression for area

    The total perimeter of a sector is 2. Find an expression for its area in terms of:
    a) Its Radius
    b) Its Angle
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    Re: Radian Measure: Finding an expression for area

    $P = 2r + r\theta$

    $A = \dfrac{r^2}{2} \cdot \theta$

    so, what have you attempted?
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    Re: Radian Measure: Finding an expression for area

    I tried solving for r using the perimeter equation,
    i.e. 2 = 2(r) + r
    r = 2/(2+)

    And then I subbed that into the area equation,
    i.e. A = (1/2)(2/2+)^2()
    And then I get
    A = (2/(2+)^2()

    But the answer on the memo is:
    a) r(1-r)
    b) 2/(2+)^2
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    Re: Radian Measure: Finding an expression for area

    Quote Originally Posted by KiaraG16 View Post
    I tried solving for r using the perimeter equation,
    i.e. 2 = 2(r) + r
    r = 2/(2+)

    And then I subbed that into the area equation,
    i.e. A = (1/2)(2/2+)^2()
    And then I get
    A = (2/(2+)^2()

    But the answer on the memo is:
    a) r(1-r)
    b) 2/(2+)^2
    Have a look here.
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  5. #5
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    Re: Radian Measure: Finding an expression for area

    $2=2r+r\theta \implies \theta=\dfrac{2(1-r)}{r}$

    $A=\dfrac{r^2}{2} \cdot \theta = \dfrac{r^2}{2} \cdot \dfrac{2(1-r)}{r} = r(1-r)$


    $2=r(2+\theta) \implies r=\dfrac{2}{2+\theta}$

    $A=\dfrac{r^2}{2} \cdot \theta = \dfrac{1}{2} \cdot \dfrac{2^2}{(2+\theta)^2} \cdot \theta = \dfrac{2\theta}{(2+\theta)^2}$
    Thanks from KiaraG16
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