



 
Hi Michael. There are many ways to solve this problem, but I'm going to show you a purely algebriac way. You'll see in this reply to Dana that I derived the equation for any regular polygon's area (A_{RP}) given its side length a (number of sides is n): So for a regular hexagon whose perimeter P is known, n=6 and a=P/6, the area of the hexagon is: [Note: You can see that I've substituted tan 30° with its exact value.] But we don't yet know what P actually is, except that it is perimeter of an equalateral triangle with area 10 square units. Of course, an equilateral triangle is also a regular polygon, so the same equation applies here. Let's use this to find the value P^{2} which we need in the equation above. [Again, tan 60° is replaced with its exact value.] So when we solve this for P^{2}, we get Now we can substitute this value of P^{2} into the earlier equation to find the value A_{H} that answers the question: Hope this helps,  


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