SOLUTION: Assume that DABC below is an equilateral triangle. If CD^(perpendicular) AB and CD = 6, what is the area of DABC? I can't draw the triangle but it's just a basic equilateral. CD

Algebra ->  Triangles -> SOLUTION: Assume that DABC below is an equilateral triangle. If CD^(perpendicular) AB and CD = 6, what is the area of DABC? I can't draw the triangle but it's just a basic equilateral. CD      Log On


   

Question 810762: Assume that DABC below is an equilateral triangle. If CD^(perpendicular) AB and CD = 6, what is the area of DABC?
I can't draw the triangle but it's just a basic equilateral. CD is the height. AB is the base.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
  
   
        AB = AC

        AB = 2AD

      Area = 1%2F2AB·CD = 1%2F2AB·6 = 3AB = 3(2AD) = 6AD

      Area = 6AD

 ADČ + CDČ = ACČ = ABČ = (2AD)Č = 4ADČ

 ADČ + CDČ = 4ADČ

       CDČ = 3ADČ

        6Č = 3ADČ

        36 = 3ADČ
        
        12 = ADČ

       √12 = AD

      √4·3 = AD

       2√3 = AD

Area = 6AD = 6(2√3) = 12√3

Edwin