If the perimeter of a closed figure increases does the area also increase? Why/why not?
Yes it does ...example $\displaystyle P_{square}=4x,Area_{square}=x^2$...if you increased it a fixed amount $\displaystyle a$ then it is plain to see that the are increases $\displaystyle P_{square_{2}}=4(x+a),Area_{square_{2}}=(x+a)^2$