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Formulas
for Two and Three Dimensional Shapes
Sentence
about formulas...
Triangles
The formula
for finding the area is 1/2 bxh.
The formula
for finding the perimeter is to add all the sides together.
If you
have a triangle with a height of 7 and a base of ten, what
is the area?
If you
have a triangle with one side measuring 7 in, one side measuring
10 in and the last measuring 8 in, what is the perimeter.
Squares
The formula to find the area of a square is (S=side) SxS.
The formula
to find the perimeter is hx4
So if
you had a square, and I of the sides were 4" long, what
is the area of the square?
Then,
if you had a square with a height of 7, what is the perimeter?
Rectangle
The formula to find the area of a rectangle is (L=length W=width)
LxW.
The fomula
to find the perimeter of a rectangle is lxw.
So if
you had a rectangle and the length was 7"long, and the
width was 3" long, what is the area of the rectangle?
Then,
if you have a rectangle with a height of 9 ft. and a legnth
of 10 ft., what is the perimeter?
Trapezoid
The
formula to find the area for this shape is hx(b1+b2).
The formula
to find perimeter of a trapezoid is to add the bases and multiply
the height by two, then add them together.
If you
have a trapezoid with a 5 cm height and two basesmeasuring
7 cm and 10 cm, what is the area?
Then,
when you have a trapezoid with a height of 20 in, a b1 of
7 in and a b2 of 12 in, what is the perimeter?
Other
2-D shapes
For all
other shapes, you split the shapes into triangles and count
the triangles. Then you find the area of all the triangles
and find the sum of them all. Then you have the area. The
perimeter is just adding all the sides.
3-D
Shapes
To find
surface area, split the polyhedron into 2-d shape and find
the individual areas of the faces. The sum of those shapes
is the object's surface area.
So, what
are is the surface area of this rectangular prism?
Volume
Before
you start on these, go back and review the 2-d shapes. You'll
see why in a moment.
Now
that your memory is refreshed, lets get at it. The universal
way to finding the volume of a prism is to find the 2-d base's
area, and muliply it by the height. See, I didn't want to
reteach
2-d shapes, so I told you to go back and review.
Try
some really quick.
Triangular
prism:
Base:
5 in=h, 10 in=b
Height:
13 in.
Rectangular
Prism:
Base:
2 cm=l, 5 cm=w
Height:
6.8 cm
Trapezoidal
Prism:
Base:
7 m=b1, 10 m=b2, h= 4
Height:
6 m
Circles
and Cylinders
Circles
are actually quite easy if you can handle pi, or 3.14.
So,
the radius is always 1/2 of the diameter, and the circumference
is always 3.14 times the diamter. So try finding the circumerence
and diamter of this facing figure:
Area isn't quite as hard as most people think.
Find the radius of the circle and square it. Then multiply
the product by pi.
Cylinders
By
far, this objective has taken the longest for me to do. Bleh,
evil objective... Well, heh. The final part: Cylinders. To
find the volume of the cylinder, all you have to do
is use the formula to find the area of a circle, and multiply
it by the height. Again. Finally, I finished this silly objective,
have a nice day....
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