Perimeter of Irregular Shapes
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.
… where the diameter of each circle is equal to one of the square's sides.
Before he can make the crop circle, Arnold needs to know the total area of his new plot
of land. First we’ll find the area of the inner square
of land. We’ll call the length of each side of the square “a”.
Now, we know that the Perimeter equals nine yards.
First we want to find out the length of one side, so we write out our equation as “a”
plus “a” plus “a” plus “a”...or put another way… 4a equals 9.
By dividing four from both sides of the equation...we get the length of “a” which equals nine-fourths…
Now we need to square “a” to get the area of our square. We square 9 fourths to get…
… eighty-one sixteenths, the area of the original plot of land.
Now onto the 4 semi-circles.
The diameter of the circle is equal to the length of the square, which if you’ll remember
… so the radius of the circle, is half of that, or nine-fourths times one-half...which
The formula for the area of a semicircle is one-half pi times the radius squared.
By plugging in nine-eighths as the radius of the circle, we get one-half pi times nine-eighths
When we square nine eighths we get 81 over 64….times one half pi….
Next we multiply 81 64ths by 1 half pi to get 81 pi over 128…the total area of 1 semicircle…
Now we add them all to get the total area…
Since we have 4 semicircles and one semicircle equals 81pi over 128, we multiply 81pi over
128 by 4 to get….324 pi over 128… the total area of all four semicircles.
We need to add the total area of the square… which is 81 16ths… to our four semicircles.
By estimating that pi equals 3.14, we can type into our nifty calculators... eighty-one
sixteenths plus 324 pi over 128 equals... thirteen point seven.
Bingo! The area of the new land parcel is 13.7 yards.
Good crop circle, Arnold. Way to stick it to your supervisor.