A regular octagon with sides of length x cm has an area 240 cm2. calculate the value of x, leaving your answer to 2 decimal places?

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Answer 1 · 2018-06-20T16:20:38

#color(blue)(x=7.05) \ \ \ \ \ # 2 d.p.

There is a formula for the area of a regular octagon.

#"Area"=2a^2(1+sqrt(2))#

Where #a# is the side of the octagon. In this case it will be #x#.

This formula can be derived using trigonometry.

We are given the area of #240"cm"^2#, so:

#2x^2(1+sqrt(2))=240#

We now need to solve for #x#:

Divide by: #2(1+sqrt(2))#

#x^2=240/(2(1+sqrt(2)))=120/(1+sqrt(2))=(120(1-sqrt(2)))/-1=-120(1-sqrt(2))#

#x=sqrt(-120(1-sqrt(2)))~~7.050221800#

#color(blue)(x=7.05) \ \ \ \ \ # 2 d.p.