A picture window has a length of 9 feet and a height of 8 feet, with a semicircular cap on each end.

Question

Window Space. A picture window has a length of 9 feet and a height of 8 feet, with a semicircular cap on each end.
How much metal trim is needed for the perimeter of the entire window?
___ft 
How much glass is needed for the opening of the window?
___ft^2

 

I'm confused on how to answer this question because I don't know what a semicircular cap is? How do I answer this question?

 

Answer 1

A semi-circle is half of a circle. The problem is saying that the window is shaped like a rectangle, with half of a circle on each end.

 

We can break the window into 3 parts to measure the perimeter and area:

 

1. A rectangle with length = 9 and height = 8

2. Two semi circles with diameter = 8 (which is the same as a full circle with radius = 4)

3. Two semi circles with diameter = 9 (with is the same as a full circle with radius = 4.5)

 

To find the total perimeter, just add the perimeter of the first circle (2*pi*4), and the perimeter of the second circle (2*pi*4.5).

 

To fine the total area, just add up the area of the rectangle (L*H), the area of the first circle (pi*4^2), and the area of the second circle (pi*4.5^2)

Answer 2

the window would look somewhat like this but with another semicircle on each side:

http://www.emjoineryservices.co.uk/wp-content/uploads/photo-218.jpg

 

it would look something like a 4-leaf clover

 

So we have L=9, H=8 for the rectangular part which makes the diameters of each semicircle equal to the L and H of the corresponding side

 

Perimeter:

2(pi)(H/2) + 2(pi)(L/2) = Perimeter

We have 2, 1/2 circles of the same diameter so we can count it as 1 full circle

plug in numbers:

2(pi)(8/2) + 2(pi)(9/2) = Perimeter

8*pi+9*pi= 53.38 ft= perimeter

 

Glass (or area):

(L*H)+(pi*(L/2)²)+(pi*(H/2)2)=area

Here we can split the window into its rectangular and circular sections with the area of each added together

9*8+3.14*4²+3.14*4.5²=area

72+50.24+63.585=185.825 ft²

 

Let me know if you need further help!