Answer:
AB = 3.3 cm
Step-by-step explanation:
The formula to find out area of a regular octagon is given by
[tex]A=2(1+\sqrt{2})a^{2}[/tex]
where a is the length of each side of the regular octagon.
Plugin A=54 into the formula
[tex]54=2(1+\sqrt{2})a^{2}[/tex]
Divide both sides by 2
[tex]\frac{54}{2} =\frac{2}{2} (1+\sqrt{2})a^{2}[/tex]
[tex]27 = (1+\sqrt{2})a^{2}[/tex]
Plugin √2 as 1.41
[tex]27 = (1+1.41)a^{2}[/tex]
[tex]27 = (2.41)a^{2}[/tex]
Divide both sides by 2.41
[tex]\frac{27}{2.41} = \frac{2.41}{2.41} a^{2}[/tex]
[tex]11.20 = a^{2}[/tex]
Taking square root on both sides
[tex]\sqrt{11.20} = \sqrt{a^{2}}[/tex]
a = 3.346
a = 3.3 cm (rounded to nearest tenth)
so, length of side AB = 3.3 cm
Answer:3.4
Step-by-step explanation:
For enginuity- just took the test
