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Mathematics
OpenStudy (anonymous):

Find the area of the regular polygon. Give the answer to the nearest tenth. decagon with side 4 cm A) 123.1 cm2 B) 129.4 cm2 C) 246.2 cm2 D) 139.8 cm2 Thanks!

OpenStudy (a_clan):

A

OpenStudy (anonymous):

A) 123.1 cm^2

OpenStudy (anonymous):

thanks both of you! Clan answered first though lol

OpenStudy (anonymous):

ill give it to you both... I didn't know I could do that!

OpenStudy (anonymous):

The area of a regular polygon is (0.5)(apothem)(perimeter), where the apothem is the distance from the center of the shape to the middle of any side. The apothem is found by the formula r=(0.5)(s)(cot(180/n)) where r is apothem, s is the length of the sides, and n is the number of sides. Thus for this problem, r=(0.5)(4)(cot(180/10))=6.155. Note that cot(x)=1/tan(x). Therefore the area is (0.5)(6.155)(10*4)=123.1, or answer A.

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