Another sample problem for Meet 4

Given a square with an equilateral triangle removed. If the square has a side of 6cm, what is the area of the figure, exactly?

(The phrase "exactly" means if we get a square root, we won't approximate it with a decimal, we'll just leave it, which is probably what they'll do on the real test, since calculators aren't allowed.)
We've got a 6x6 square with a triangle cut out. Let T= Area of the Triangle. Area of figure = 36-T. There are 3 ways to solve the triangle - A)Pythagorus, B)Heron, or C) memorize that equiateral triangle. If memorized, side of 1 means height of ½√3, a side of 6 means a height of 3√3 so the area is ½ bh = ½ x 6 x 3√3 = 9√3
Or use Heron √(s(s-a)(s-b)(s-c)) where s = semi-perimeter = 9 T =√(9(9-6)(9-6)(9-6))
T=√(9*3*3*3)=3*3√3 =9√3
So A = 36-9√3