1: Draw your hexagon, so you can see what is going on.
2: Construct lines from the center point to each of the vertices, you now have 6 isosceles triangles.
3: Divide 360' by 6 to get the angle at the top vertex of one of the triangles = 60'
4: Since these are isosceles triangles, you know the base angles are equal, so these are both 60'
5: This tells you that you are in fact dealing with equilateral triangles not isosceles, so the all three vertices are 40cm
6: Now draw a diagram of an equilateral triangle with three angles of 60' and lengths of 40cm
7: Drop a perpendicular from the vertex to the opposite side - this is your Apothem. This perpendicular actually creates two right angled triangles, and bisects the side. So now you have another triangle - yip you guessed it - Draw a diagram.
8: Draw a diagram of a right angled triangle, with hypotenuse of 40, angles of 30, 60 and 90 and shortest length of 20
9: Let A (for Apothem) be the unknown side - use pythagorean theorem to solve.
10 40^2 = 20^2 + A^2
1600 = 400 + A^2
1200 = A^2
square root of 1200 = A approximately 34.6414cm
I hope this helps
K6Math
2: Construct lines from the center point to each of the vertices, you now have 6 isosceles triangles.
3: Divide 360' by 6 to get the angle at the top vertex of one of the triangles = 60'
4: Since these are isosceles triangles, you know the base angles are equal, so these are both 60'
5: This tells you that you are in fact dealing with equilateral triangles not isosceles, so the all three vertices are 40cm
6: Now draw a diagram of an equilateral triangle with three angles of 60' and lengths of 40cm
7: Drop a perpendicular from the vertex to the opposite side - this is your Apothem. This perpendicular actually creates two right angled triangles, and bisects the side. So now you have another triangle - yip you guessed it - Draw a diagram.
8: Draw a diagram of a right angled triangle, with hypotenuse of 40, angles of 30, 60 and 90 and shortest length of 20
9: Let A (for Apothem) be the unknown side - use pythagorean theorem to solve.
10 40^2 = 20^2 + A^2
1600 = 400 + A^2
1200 = A^2
square root of 1200 = A approximately 34.6414cm
I hope this helps
K6Math