Given: ∆AFD, m ∠F = 90° AD = 14, m ∠D = 30° Find: Area of ∆AFD

Answer:[tex]\frac{49\sqrt{3}}{2}[/tex]Step-by-step explanation:This is a 30-60-90 triangle.  The sides of this triangle can be represented as t (across from the 30° angle since it is the smallest side), 2t (across from the 90° angle since it is the largest side), and t√3 (across from the 60° angle).Since F is the right angle, this means that AD is across from F and is the hypotenuse.  The hypotenuse of a right triangle is the longest side; this means that 2t = 14, so t = 7.  This also tells us that t√3 = 7√3.This means that the height and base of the triangle are 7 and 7√3.  Using the formula for the area of a triangle, we haveA = 1/2bh = 1/2(7)(7√3) = 1/2(49√3)[tex]=\frac{49\sqrt{3}}{2}[/tex]