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!

Question

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!

a_clan · Answer

A

anonymous · Answer

A) 123.1 cm^2

anonymous · Answer

thanks both of you!  Clan answered first though lol

anonymous · Answer

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

anonymous · Answer

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.