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.