Urgent CALCULUS
posted by Derek .
So, I haven't posted in a while...but now I am stummped! Only question I can't get today!
A team of students seeks to make a flag representing their commitment to the earth. They will be using a green triangle inscribed in a yellow semicircle. Find the maximum area of the triangle inscribed in a semicircle of radius r.
So I know you somewhere have to use 1/2pir^2...but then what?
THANKS!

Sounds like a common sense kind of problem
The largest area is obtained with a largest possible base and a largest possible height.
Clearly the diameter is as large as you could make a base, and the height cannot be any larger than the radius at from the centre of the semicircle
so the largest area would be 1/2(2r)(r) = r^2 
You could try putting that if the base is = r and the height is r^2 and the triangle is isosceles, you will get the largest area. I think!
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