I initially had to use the attached diagram to solve problems related to a concert venue.So I created a formula for perimeter and area and used these to create a formula for area with x as the only variable.I used differentiation to find the value of x when the area is at a maximum.
Value for Pi given as 22/7
P=4xy + 2x +Pix
y into area formula to give a= px -25x^2/7
The final question i'm stuck on asks "Critically examine the shape of the concert venue with this maximum area and comment on it.Make 2 suggestions for improving the concert venue given that the perimeter must remain the same"
I've solved these to
a =-25x^2/7 + px and x =7p/50
The Attempt at a Solution
I'm a little stuck on what the final question is asking, my intial observations are that a circle would give the maximum area based off a fixed perimeter and that while a square offers more area than a rectangle, now it is used in conjunction with a semi-circle the rectangle provides the best solution.As the circle is linked to the x value, if you reduce x to make a square the area of the circle is reduced.
Thanks for reading