Question

A yield sign is an equilateral triangle, with side length 34 inches. How many square inches of material is needed to make a sign?

Answer 1

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$\sqrt{3}$
so the height of the equilateral triangle is 17$\sqrt{3}$

A = (1/2)(34)(17$\sqrt{3}$)
A = 500.56 square inches