1. ## Radian Measure: Finding an expression for area

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

2. ## Re: Radian Measure: Finding an expression for area

$P = 2r + r\theta$

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

so, what have you attempted?

3. ## Re: Radian Measure: Finding an expression for area

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

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

But the answer on the memo is:
a) r(1-r)
b) 2Ø/(2+Ø)^2

4. ## Re: Radian Measure: Finding an expression for area

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

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

But the answer on the memo is:
a) r(1-r)
b) 2Ø/(2+Ø)^2
Have a look here.

5. ## Re: Radian Measure: Finding an expression for area

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

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

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

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