Re: Area problem

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: : Huge triangle ABC has an area of 20,000,000 square feet. : : D is on AB, E is on BC and F is on CA. : : AD = 1/16th of AB, BE = 1/16th of BC, CF = 1/16th of CA. : : Find area of triangle DEF. : : Thank you. : I will get you started. : 1. Draw a picture. Obviously you could put A, B and C anyplace, but it will be easier to see my explanation if we are both looking at the same picture. So, I put A at the top, B at the right end of the base, and C at the left end of the base. Now put D, E, and F as described in your problem. Next, drop a line from A, perpendicular to BC, meeting BC at point G. Also drop a line from F perpendicular to BC, meeting BC at H. : 2. Let's call the length of BC = a, AC = b, and AB = c. Let's call the height AG = h, and the height of the small triangle (FEC) FH = x. : 3. Notice that the two triangles FEC and ABC share the same angle {<ACB}. What is the sine of that angle? sin{<ACB} = h/b = x/((1/16)b) : Think about that & you will see that you now have enough information to calculate the area of triangle FEC. : You can calculate the areas of triangles EDB and DFA by the same method. : Then what? : Got it?

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