Question

The area of the regular octagon is approximately 54 cm2. What is the length of line segment AB, rounded to the nearest tenth?

Answer 1

Answer:3.4

Step-by-step explanation:

For enginuity- just took the test

Answer 2

Answer:

AB = 3.3 cm

Step-by-step explanation:

The formula to find out area of a regular octagon is given by

$A=2(1+\sqrt{2})a^{2}$

where a is the length of each side of the regular octagon.

Plugin A=54 into the formula

$54=2(1+\sqrt{2})a^{2}$

Divide both sides by 2

$\frac{54}{2} =\frac{2}{2} (1+\sqrt{2})a^{2}$

$27 = (1+\sqrt{2})a^{2}$

Plugin √2 as 1.41

$27 = (1+1.41)a^{2}$

$27 = (2.41)a^{2}$

Divide both sides by 2.41

$\frac{27}{2.41} = \frac{2.41}{2.41} a^{2}$

$11.20 = a^{2}$

Taking square root on both sides

$\sqrt{11.20} = \sqrt{a^{2}}$

a = 3.346

a = 3.3 cm (rounded to nearest tenth)

so, length of side AB = 3.3 cm