Question

Hi!

I am here with a handful of geometry questions today. Please answer the question based off the image(s) below.

If you are not sure of the answer please leave a comment, DO NOT ANSWER THE QUESTION UNLESS YOU KNOW THE ANSWER. Please don't take me points! Thanks for understanding.

Anyways, please show all of your work and explain your thinking! Make sure to do both of them! Thanks!

Answer 1

9514 1404 393

Answer:

1. area DEF = 2π cm²

2. arc JK = 2π cm

Explanation:

1. The area is given by ...

A = 1/2r²θ . . . . . where r is the radius and θ is the central angle in radians

Your sector has an area of ...

A = (1/2)(3 cm)²(80(π/180)) = (1/2)(9 cm²)(4/9π)

A = 2π cm²

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2. The length of an arc is ...

s = rθ . . . . . . . where r is the radius and θ is the central angle in radians

s = (5 cm)(72(π/180)) = (5 cm)(2/5π)

s = 2π cm . . . arc length

_____

Additional comment

There are π radians in 180°, so an angle in degrees can be converted to an angle in radians by multiplying by π/180°. (The units of degrees cancel, leaving a pure number. "Radians" have no units.)