ADVANCED EXERCISES

(4)

 Using the following diagram:

 a) Solve for x.

 b) Find the area of triangle ABC.

 c) Derive a general formula for the area of equilateral triangles in terms of s, 
     one of the sides

a) Solving the first right triangle gives you a hypotenuse of 5.  Solving 
the second right triangle gives you a hypontenuse of 13.  Knowing that 13 is 
the length of all of the sides of triangle ABC and that side AC must be bisected 
by the altitude from B, 
	132 = (13/2)2 + x2
	169 = 169/4 + x2
	(3*169)/4 = x2
	x = 13/2

b) Knowing that the base is 13 and the height is 13/2,
we apply the formula Area = 1/2 (base*height) and get Area of triangle ABC = 
169/4.

c) Using a method similar to b, or just through logic, one sees that a general formula for the
area of an equilateral triangle is s2/4.