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Area of an Irregular Shape 36353 Views


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Description:

We feel really bad for these irregular shapes. We can only imagine how they must feel. Perhaps we could recommend a high-fiber diet? That might help to make them more...regular.

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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…

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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