Question

NO LINKS!!!! URGENT HELP PLEASE!!!!!!

11. Find the area of a regular octagon inscribed in a circle of radius 40 cm.

12. Find the area of a regular 12-sided polygon inscribed in a circle of radius 8 cm.

Answer 1

11) $3200\sqrt{2}$ cm²

12) 192 cm²

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Area  A  of  n- sided regular polygon inscribed in a circle of radius r  is given by formula:

• $A=(n/2)r^2sin(2\pi/n)$

11......................

In this case we have n = 8 and r = 40 cm.

Substitute values into formula to get:

• $A=(8/2)(40)^2sin(2\pi/8)$
• $A=4*1600*sin(\pi/4)$
• $A=4*1600*\sqrt{2} /2$
• $A=3200\sqrt{2}$

12........................

In this case we have n = 12 and r = 8 cm.

Substitute values:

• $A=(12/2)(8)^2sin(2\pi/12)$
• $A=6*64*sin(\pi/6)$
• $A=384*(1/2)=192$