| Ordered
Pairs
Have
you ever ordered pizza? How about ordered pairs?
Mathematics:
Geometry and Spatial Sense, Standard 3, Objective one:
Represents and applies geometric properties and relationships
to solve real life and mathematical problems.
Technically, what the above in bold means that the purpose
of learning geometric shapes and figures, and learning how
to use plains is a required element of teaching in a Florida
school. It is also required for you to learn (bummer, huh?)
to pass middle school. The geometry sense does help in real
life, but we'll get to it later…
Example
1: 2D Plains
In a 2-D plain, the only points are X and Y. You use X
and Y to find objects and figures on a plain. So, say you
want to get to a friends house, and you will then travel to
the store with them. If you friends house is three blocks
east, then you will travel 3 blocks on X, the bottom axis.
The store is then 4 blocks north; you travel four blocks on
the Y-axis. This totals up to 7 blocks. If you suddenly have
the urge to call up your friend and cancel it, but still go
to the store, and in the shortest possible route, you can
use the Pythagorean Theorem (A squared + B squared = to C
squared, or in this case X squared + Y squared = the shortest
distance squared). So, since X squared is 9, and Y squared
is 16, they total 15. Then you find 15's square route, which
is 3.87.So the shortest possible route is 3.87 blocks, instead
of 7.
Example
2: 3D Plains
3D plains are essentially the same thing as 2D ones except
for the extra dimension. You now have to deal with the Z-axis,
which ascends into the air. So, say (bear with me) you're
in a field with fruit trees. You're at the Banana tree, but
you want to get to the Apple tree, then the Orange tree, and
finally climb it. If it's 5 meters to the Apple tree from
the banana tree on the X-axis, and 10 meters from the apple
tree to the orange tree on the Y-axis. You then climb the
tree 3 meters on the Z-axis. Got it? Good. This totals 18
meters. Again, you can use the Pythagorean Theorem to find
the shortest distance from travel to the trees. Again, X squared
+ Y squared is equal to 125. The square route of 125 is 11.2.
Add 11.2 to 3 and you get 14.2 meters. This is the shortest
possible distance without hovering.
Example
3: Area and Perimeter
Perimeter is the total length of all the sides in a shape.
Finding it in geometric figures is actually quite easy if
you remember this: add all the sides. Say a square has 4-inch
sides. Since a square has four sides, you multiply 4 by 4
and get 16. 16 inches is the perimeter of the square. For
other polygons, you do just the same. If a perfect hexagon
has sides of 10 inches, multiply 10 by 6 and get a perimeter
of 60 inches.
Area is,
unfortunately harder. It is the total surface space of an
object. That is what people are referring to when you hear
square feet or square inches. To keep this short and simple,
I will just simply list formulas for all shapes up to Trapezoids.
After that, I'll go in depth with other shapes.
Formulas
Triangle:
½ of B x H
B=4 ft
H=6 ft
½ B=2
6x2=12
A=12 square ft.
Square/Rectangle:
L x W
L=7 in.
W=6 in.
7x6=42
A=42 square in.
Parallelogram:
B x H
B=4 m
H=12 m
4x12= 48
A=48 square m
Trapezoid:
½ (B1+B2) x H
B1=4 mi.
B2=6 mi.
4+6=10 ½= 5
H=6 mi.
5+6=11
A=11 square mi.
Circle:
pi x r squared
Pi= 3.14 ft
R= 4 ft
3.14 x 4= 12.56
A= 12.56 ft squared
This covers
the main objects. Any object with 5 or more sides is actually
quite simple. Take a hexagon for example. It has four triangles.
You can do this by counting or subtracting the number of sides
by two. Now find the area for each of these triangles and
add them. That is the area of the Hexagon. That covers this
section. Now for the bloody test:
Bloody
Test
1. Joe
wants to get to the Hot Dog stand. He's in the bathroom. Joe
must walk 5.6 yards east and 100 yards north. How many yards
must Joe travel? If Joe finds the shortest possible route,
how many yards less will he walk than the first route?
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