Answer:
7,725.48 cm² (2 d.p.)
Step-by-step explanation:
To determine the area of a regular polygon given its side length, we can use the following formula:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Area of a regular polygon}}\\\\A=\dfrac{ns^2}{4\tan\left(\dfrac{180^{\circ}}{n}\right)}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$n$ is the number of sides.}\\ \phantom{ww}\bullet\;\textsf{$s$ is the side length.}\end{array}}[/tex]
In this case:
Substitute the values into the formula and solve for A:
[tex]A=\dfrac{8\cdot 40^2}{4\tan\left(\dfrac{180^{\circ}}{8}\right)}\\\\\\\\A=\dfrac{8\cdot 1600}{4\tan\left(22.5^{\circ}\right)}\\\\\\\\A=\dfrac{12800}{4\tan\left(22.5^{\circ}\right)}\\\\\\\\A=\dfrac{3200}{\tan\left(22.5^{\circ}\right)}\\\\\\\\A=7725.48339959...\\\\\\\\A=7725.48\; \sf cm^2[/tex]
Therefore, the area of a regular octagon with sides measuring 40 cm is:
[tex]\Large\boxed{\boxed{7725.48\; \sf cm^2}}[/tex]
