Find the area of the regular octagon if the apothem is 3 cm and a side is 2.5 cm? Round to the nearest whole number.

i really dont understand the whole thing.

2 Answers
天皓 利. · Stefan V.
Feb 24, 2018

Should be #"30 cm"^2#.

Explanation:

The apothem is a line segment from the center to the midpoint of one of its sides. You can first divide the octagon into #8# small triangles. Each triangle has an area of

#"2.5 cm"/2 xx "3 cm" = "3.75 cm"^2#

Then

#"3.75 cm"^2 xx 8 = "30 cm"^2#

is the total area of the octagon.

Hope you understand. If not, please tell me.

Nam D.
Feb 24, 2018

I get #30 \ "cm"^2#.

Explanation:

Given the apothem length, the area of a regular polygon becomes

#A=1/2*p*a#

#p# is the perimeter of the regular polygon

#a# is the apothem of the regular polygon

Here, we get #p=8*2.5=20 \ "cm"#, #a=3 \ "cm"#.

So, plugging in the given values, we get

#A=1/2*20 \ "cm"*3 \ "cm"#

#=10 \ "cm" * 3 \ "cm"#

#=30 \ "cm"^2#

So, the regular octagon will have an area of #30 \ "cm"^2#.

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