You are given a triangle with a fixed perimeter but you want to maximise the area. What shape will it be? Prove it.

Next you are given a quadrilateral with fixed perimeter and you want to maximise the area. What shape will it be? Prove it.

Not sure how to do this, my thoughts would be that it is a right angled triangle, but not sure how to prove it. Did try various methods but got no where, as the variables were different when I compare it to an iscoleces, equilateral etc.