Question 853677

The diameter of the semicircle is equal to the width of the rectangle.  You'd still use the height in the calculations along the way.

If the height of the rectangle part was h and the width was x, then the perimeter would be 
(length of 3 rectangle sides) + (curved part from semicircle) = 

(h+h+x) + ( (1/2) 2 π r )
(h+h+x) + ( π r )
(2h+x) + ( π (x/2) ) = 35

You can use this to get h in terms of x, or vice versa.  Then plug it into the expression for area to get things in terms of width.

2h+x = 35 - π(x/2)
2h = 35 - π(x/2) - w

h = 17.5 - π(x/4) - (x/2)

The area would be

(area of rectangle) + (area of semicircle) = 

h*x + ((1/2)π r^2)
h*x + ((1/2)π (x/2)^2)
h*x + (π x^2)/8

Take the expression for h and plug it in here to get everything in terms of x.


[17.5 - π(x/4) - (x/2)]x + (π x^2)/8

A(x) = 17.5x-π(x^2/4)-(x^2/2) +
(π x^2)/8

:)