what is the area of a octagon with a radius of 5

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Ellie, A polygon does not have a radius. However if you are suggesting the circle that circumscibes the octogon has radius 5 you must recall that the formula for the area of a polygon is A = 1/2 a P where a is the length of the apothem and P is the perimeter of the polygon.. To find perimeter and the apothem of your octagon you will need to solve 2 simple trig problems . The needed triangle will have the radius as its hypotenuse and the angle opposite the apothem will be 62.5 degrees  so 5sin62.5 will be your apothem and 2( 5cos 62.5) will equal a single side measure thus multiply this value by 8 to obtain  your perimeter. Hope this helps you!