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Hi Tracy, The area of the regular pentagon will be the same as the sum of the areas of the five identical isosceles triangles you can form by drawing in the radii to the vertices of the pentagon. Now you can see that you know the lengths of all three sides of each individual triangle. Heron's Formula can be used to determine the area of the triangle when you know all three sides:
You could also determine the size of the central angle (C) which is also the vertex angle of each triangle formed. and then use Area=(1/2)ab*sinC. Just remember that after you find the area of one triangle, you must multiply by 5 to get the area of the entire pentagon. This is just a couple of the ways in which this problem could be solved. Hope this helps, Leeanne
Tracy, The area is 1/2 base times altitude of the triangle that consists of one of the pentagon's sides and the radii to the two endpoints of that side. You multiply that area by 5 for the area of the pentagon. I suppose that you can use 6 as the length of the side, but the side really has length 10*sin (36 degrees), which equals about 5.8779. The altitude (which is the distance from the centre of the pentagon to the side) is 5*cos (36 degrees), (which equals about 4.0451). (If you use the Pythagorean theorem with a triangle whose sides are 5, 5, and 6, the altitude to the base is then 4 instead of the more exact 4.0451. In fact, the triangle made up of half a side, altitude and radius is a 345 right triangle.) Chris  


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