2 Answers

Artem Novikov · Answer 1 · 2020-08-07T22:26:03+0000

To work out the length of an arc, we use the following equation:

$arclength=(angle)/(360)* 2\pi r$ (r stands for radius)

So just substitute in the values to get the arc length of the first sector:

(angle = 40, radius = 12)

$arclength=(angle)/(360)* 2\pi r$

$arclength=(40)/(360)* 2\pi 12$

$arclength = (8)/(3) \pi$

For the other sector, the angle will also be 40, since opposite angles are the same. So to get the arc length, we substitute in:

(angle = 40, radius = 5)

$arclength=(angle)/(360)* 2\pi r$

$arclength=(40)/(360)* 2\pi 5$

$arclength=(10)/(9)\pi$

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Now to get the perimeter, we add up all of the arc lengths and side lengths:

$Perimeter =(8)/(3)\pi+(10)/(9)\pi + 12 + 12 + 5 + 5$

$Perimeter = (34)/(9)\pi +34$

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Answer:

Perimeter =
$(34)/(9)\pi +34$ cm or 45.87cm rounded to 2 decimal places.

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