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PLEASE HELP! Find the area of the regular polygon(shown below). Answer in reduced radical form. Show your steps.

PLEASE HELP! Find the area of the regular polygon(shown below). Answer in reduced-example-1
User Yanet
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1 Answer

4 votes
this is weird tho but since it's regular that means it's equiangular/equilateral. So every angle is 60°.
The 8 is half of of the triangle (I think??) so you'd have to turn it to 16 so it'll be full. It'll then be an altitude so I'll make a right angle.
Now you've got two congruent triangles, both of them are 30-60-90 special right triangles so you can use sohcahtoa.

Use the 60° angle to find the hypotenuse

sin(60) = 16/h
(h)sin(60) = 16
/sin(60) on both sides
18.48 is the answer

If you want that as a radical then its somewhere around 3√2

That means every side is 3√2 because it's regular so do 3√2 x 3√2 which i think is 12 ??? Maybe???? Idk sorry
User Aaronjkrause
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