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Perimeter of Irregular Shapes 4864 Views
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Description:
Want to figure out the area and perimeter of irregular shapes? Break them down into regular shapes. For example, a flower can be broken down into semi-circles and a square. Don't try to do it the long way—the flower may wilt before you're done.
Transcript
- 00:04
Perimeter of Irregular Shapes, a la Shmoop. Arnold the Alien buys a square patch of land
- 00:10
with a perimeter of 9 yards. He’s a small alien.
- 00:13
His supervisor Bill tells him that the land is not nearly interesting enough for a crop
- 00:18
circle. Arnold immediately goes out and buys four
- 00:24
semicircular plots of land around the square…
Full Transcript
- 00:26
… where the diameter of each circle is equal to one of the square's sides.
- 00:32
Before he can make the crop circle, Arnold needs to know the total area of his new plot
- 00:37
of land. First we’ll find the area of the inner square
- 00:40
of land. We’ll call the length of each side of the square “a”.
- 00:44
Now, we know that the Perimeter equals nine yards.
- 00:48
First we want to find out the length of one side, so we write out our equation as “a”
- 00:53
plus “a” plus “a” plus “a”...or put another way… 4a equals 9.
- 01:00
By dividing four from both sides of the equation...we get the length of “a” which equals nine-fourths…
- 01:07
Now we need to square “a” to get the area of our square. We square 9 fourths to get…
- 01:15
… eighty-one sixteenths, the area of the original plot of land.
- 01:21
Now onto the 4 semi-circles.
- 01:23
The diameter of the circle is equal to the length of the square, which if you’ll remember
- 01:27
was nine-fourths…
- 01:28
… so the radius of the circle, is half of that, or nine-fourths times one-half...which
- 01:41
equals nine-eighths.
- 01:43
The formula for the area of a semicircle is one-half pi times the radius squared.
- 01:50
By plugging in nine-eighths as the radius of the circle, we get one-half pi times nine-eighths
- 01:56
squared…
- 01:58
When we square nine eighths we get 81 over 64….times one half pi….
- 02:04
Next we multiply 81 64ths by 1 half pi to get 81 pi over 128…the total area of 1 semicircle…
- 02:14
Now we add them all to get the total area…
- 02:17
Since we have 4 semicircles and one semicircle equals 81pi over 128, we multiply 81pi over
- 02:24
128 by 4 to get….324 pi over 128… the total area of all four semicircles.
- 02:33
We need to add the total area of the square… which is 81 16ths… to our four semicircles.
- 02:39
By estimating that pi equals 3.14, we can type into our nifty calculators... eighty-one
- 02:45
sixteenths plus 324 pi over 128 equals... thirteen point seven.
- 02:50
Bingo! The area of the new land parcel is 13.7 yards.
- 02:56
Good crop circle, Arnold. Way to stick it to your supervisor.
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