text: geometry ? a student in your class is confused about how to find the area and perimeter of two different polygons. they have asked you for help. your task is to explain in detail how to find the area and perimeter of the two different polygons. problem #1) a regular hexagon with apothem of 8ft #2) a regular pentagon with radius of 5m. if you draw on the apothem to each corner of the shape then you can make 6 isosceles triangles. if you split these in half then you get 2 right angled triangles. you can then use pythagoras theorum to find the height ( - you know the length of the hypotenuse as it is the apothem, and you can work out the angle by dividing 360 by 12.) you can then find the perpendicular height between the mid-point of one side and the centre of the shape. you can use this to find the area of eahc isosceles traingle (1/2 base x height) and simply multiply this by 6 to find the area of the whole shape. the same process can be done with the pentagon.  and for each you can use the values calculated to find the perimeter.