A = (1/2)base*height
Since this is an equilateral triangle each side is 34 inches, the altitude bisects the base into two 17 inch segments
There is now a right triangle with a base of 17 inches and a hypotenuse of 34 inches, so the pythagorean theorem (a^2 + b^2 = c^2) can be used
17^2 + b^2 = 34^2
or b^2 = 34^2 - 17^2
b^2 = 867 (take the square root of both sides)
b = 17[tex] \sqrt{3} [/tex]
so the height of the equilateral triangle is 17[tex] \sqrt{3} [/tex]
A = (1/2)(34)(17[tex] \sqrt{3} [/tex])
A = 500.56 square inches
