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Question One

## Homework Statement

This norman window is made up of a semicircle and a rectangle. The total perimeter of the window is 16 cm. What is the maximum area?

**

* * <<< Semicircle

*****

| | <<< Rectangle

L | |

______

D

## Homework Equations

P (total) = 2L + D + (pi * d)

A (total) = D * L + (pi(d/2)^2)/2)

## The Attempt at a Solution

What I did was using this equation:

16 = 2L + D + ((pi * d)/2)

L = 8 - d/2 - ((pi * d)/4)

A = D (8 - d/2 - ((pi * d)/4)) + (pi (d/2)^2)/2)

A = 8d - (d^2)/2

A' = 8 - d

Let 0 = A' to find critical value

then 8 = d.

When I sub that back into the original equation, I get L as a value less than 8, which doesn't make sense. (I think it works out to be L = 4 - pi)

I'm pretty much lost, sorry if this is too messy to read, any help would be appreciated. Thanks