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.

Question

i really dont understand the whole thing.

Ella Armstrong · Accepted Answer

Should be #"30 cm"^2#.

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.

Sadie Allen · Answer

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

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#.

Wyatt Anderson · Answer

undefined To find the area of the regular octagon, we can use the formula:

$$ \text{Area} = \frac{1}{2} \times \text{apothem} \times \text{perimeter} $$

Given that the apothem ($a$) is 3 cm and the side length ($s$) is 2.5 cm, we can first find the perimeter ($P$) of the octagon:

$$ P = 8 \times s = 8 \times 2.5 $$

Then, we can plug the values into the formula to find the area:

$$ \text{Area} = \frac{1}{2} \times 3 \times (8 \times 2.5) $$

$$ \text{Area} = \frac{1}{2} \times 3 \times 20 $$

$$ \text{Area} = \frac{3 \times 20}{2} $$

$$ \text{Area} = \frac{60}{2} $$

$$ \text{Area} = 30 $$

Rounding to the nearest whole number, the area of the regular octagon is 30 square centimeters.