find the perimeter of the shaded region. help :)?

Question

figure link: http://i11.photobucket.com/albums/a189/sanazmovies/perimeter.jpg
(made on paint.. hah)

In the figure above, a rectangle is intersected by a semicircle. What is the perimeter of the shaded (the blue) region?

choices:
a: 22 + 4pie
b: 20 + 8pie
c: 40 + 4pie
d: 50 + 8pie
e: 100 + 16pie

can someone explain to me? thanx :)

Answer 1

Perimeter of a circle = 2 *pi* radius or = pi *diameter

From your picture the diameter of that semicircle = 8

so the perimeter of the circle = 8 * pi

perimeter of semicircle (half circle) = 8*pi / 2 = 4* pi

Also, you can find the radius of the circle = diameter/2 = 8/2= 4

The Width of that rectangular = 1+ radius = 1+4 = 5

The two bottom short edges = the length of the rectangular - diameter of the semicircle = 10-8=2

The perimeter of the shaded area = Length of the rectangular + 2 * width + two bottom short edges + perimeter of the semicircle = 10+2*5+2+4*pi=22 + 4* pi

the answer is a.

Have fun !

Answer 2

Perimeter Of Shaded Region

Answer 3

The answer is A: 22 + 4pi

There are two unknowns, one is the radius of the circle which is 8 /2 = 4 = Radius. The other one is the side perimeter of the rectancle which is Radius + 1 = 4+1 =5.

Just the perimeter around the rectangle is 10 + 5 + 5 + 1 + 1 = 22.
The perimeter (Circumference of half the cirlcle is 2piR / 2. Dividing by 2 because we just want half of it. So its 2pi4 / 2 = 8pi/2 = 4pi.

Now add all of them up which equals to 22 + 4pi

Answer 4

Ok.. the box is 10 across... and the circle is 8 across (or 4 for radius) so the semicircle is 4 high .. + 1 makes the box 5 high..

Perimeter of blue is 10 + 2*5 + 2*1 + perimeter of the semicircle..

the Perimeter of a full circle is 2*pi*r, so for half a circle it is pi*r..

in this case r is 4 (half of 8) so... 10 + 10 + 2 = 22 + 4pi

so your answer is a.

Answer 5

Here goes. (First of all, let's have # represent pi-I do not have a pie symbol!)

Circumfrence of a rectangel is base plus height times 2
Circumfrence of a circle is 2#r (2 'pi' times radius).

The circle on your drawing has a radius of 4 (half of the 8 you labeled on that side of the drawing. So the circumfrnece of that circle would be 2#4 --> This equals 8# (eight pi). Since we only want half of the entire circumfrence we will divide in half. The length of that is now 4#.

When we add the top, (10), plus both sides, (5 each), plus the left over on each side of the cirlce on the bottom, (1 on each side), we have a total of 22.

Now, the 22 from the rectangle and the 4# from the circle make for 22 + 4#

Therefore, the answer is:
a. 22 + 4 pi

Good Luck!

Answer 6

Perimeter of determine = advert + DE + EB + curved floor AB to discover advert advert = OA – OD -------------(OA = 12 radius) component of triangle DOE = a million/2 OD × OE = 24 OD = 24 × 2 / 6 = 8 advert = 12 – 8 = 4 to discover DE This area is hypotenuse of triangle DOE components 6 and eight so DE^2 = 8^2 + 6^2 DE = 10 to discover EB EB = OB – OE = 12 – 6 = 6 to discover curved floor AB = a million/4 perimeter of circle = a million/4 × 2 pi r = a million/2 pi × 12 = 6 pi required perimeter = 4 + 10 + 6 + 6 pi = 20 + 6 pi.

Answer 7

Me sis is in geometry! :)

the circumference of the whole circle would be the diameter (8) times pi. But since it is half a circle, it is 4 pi. then it is simple adding and subtracting by looking at the lengths in the picture (which is gorgeous!). so you get 10+(10-8=2)+(4+1=5)+(4+1=5)=10+2+5+5=22+4 pi!!!!
(the answer is A)