help me solve this word problem please

Question

A stained-glass window is being designed in the shape of a rectangle surmounted by a semicircle, as shown in the figure. The width of the window is to be 3 feet, but the height h is yet to be determined. If 23 ft2 of glass is to be used, find the height h. (Round your answer to two decimal places.) 

 

I have tried separating the figure into two different figures a rectangle and a semicircle. I'm thinking I need to add the two areas together and set them equal to 23. 

 

3 x + π(1.5 )² = 23
x=6.3
x+1.5=h
6.3+1.5=7.81

 

I enter my answer on my homework but it tells me I'm wrong and I don't know what I'm doing wrong. 

Answer 1

I'm not sure where you get the x + 1.5 = h

 

if h is the height of the window, the area of the window is 3h

 

the area of the semicircle is half of what you wrote. π(1.5)² is the area of a full circle, so multiply by 1/2

 

you get

 

3h + (π/2)(1.5)² = 23

 

Do you get h = 6.49 feet?