Question

The perimeter of a sector is 20 units. If the length of the intercepted arc is 10 units, find the area of the sector.

Answer 1

Perimeter=r+r+s=2r+s

Answer 2

or P = r theta + 2 r

Answer 3

Yes that as well, from s=rθ
\[20=2r+\theta r...(1)\]
Area,
\[A=\frac{1}{2}r^2 \theta...(2)\]

Answer 4

\[P=2r+\theta r~~~~~s=r \theta \\ \\ 20=r(2+\theta)~~~10=r \theta \\ \\ r=\frac{20}{2+ \theta}\]
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\[10=\frac{20 \theta}{2+\theta} \\ \\ \theta=2\]
\[r=5\]
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From area,
\[A=\frac{1}{2}r^2 \theta \\ \\ \]

Answer 5

Thank you so much! I was a bit confused in the problem awhile ago.

Answer 6

yw :)