Use the method of lagrange multipliers to minimize the function subject to the given constraint. (round your answers to three decimal places.) minimize the function f(x, y) = x2 + 3y2 subject to the constraint x + y ? 1 = 0.

The Lagrangian for this problem is



and has partial derivatives



Set each partial derivative equal to 0 and solve for and :



Subtracting the second equation from the first, we get



and subtracting this from the third equation yields



which means



So a critical point occurs at (or (0.750, 0.250)). The minimum value would then be .

Regular polygon area = n*side^2 / (4 * tan (180/n))
where "n" is number of sides
The formula is dependent on the side^2 term,
So, if we have an octagon that has sides 4 times as large, that means the area will be sixteen times larger.
side^2 = 4^2 = 16
So we multiply 25 cm^2 by 16 and we get
400 square centimeters.

Source:
http://www.1728.org/polygon.htm