How do you find the answer to part a and what is the answer?

50ft!

Step-by-step explanation:

The smallest length of streamer that will go around the entire perimeter of the room is equal to the perimeter of the room. To find the perimeter, we add the lengths of each side of the room. Not all of the walls are labelled with a length, so we need to find these missing lengths before we can add. If we look at the bottom of the room, we can see that the total width must be 8′+2′+2′=12′.

Now that we know the width of the room, we can find the diameter of the half- circle section on the top. The diameter is the total length minus the 6′ and 2′ foot sections to the right. Therefore, the diameter of the half- circle is 12′−6′−2′=4′ and the radius is 2′. The circumference of a circle is 2′⋅πr but we only have half of a circle so the circumference of the half- circle is half of 2πr or just πr. Substituting r=2′ results in πr=2π≈6.28′.

To find the length of the long wall on the right we subtract the 2′ section at the top, from the length of the side, which is 10′. Therefore, the long wall on the right is 8′.

Now we need to find the circumference or perimeter of the circle. The fully labelled dimensions are below.

A geometric figure.

Staring in the lower left vertex, a figure has a side that goes up 10 feet, has a semicircle going to the right with a radius of 2 feet, goes to the right 6 feet, down 2 feet, right 2 feet, down 8 feet, left 2 feet, up 2 feet, left 2 feet, down 2, feet, left 8 feet back to the original point.

Therefore, the perimeter of the room is

6.28′+6′+2′+2′+8′+2′+2′+2′+2′+8′+10′=50.28′

which we'll round to 50′.