Math cps final

GEOMETRY
Gen Goeb
Math Ed
Middle & Secondary
Ages 11-18

2 Dimensional Shapes
MORE
SHAPES

3 Dimensional Shapes
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The Square
A square has equal sides and every angle is a right angle (90 )
Also opposite sides are parallel.
A square also fits the definition of a rectangle (all angles are 90 ),
and a rhombus (all sides are equal length).
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The Rectangle
A rectangle is a four-sided shape where every angle is a
Right angle (90 ).
Also opposite sides are parallel and of equal length.
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Equilateral Triangle
Three equal sides
Three equal angles, always 60°
Isosceles Triangle
Two equal sides
Two equal angles
Scalene Triangle
No equal sides
No equal angles
Equilateral, Isosceles and Scalene TRIANGLES
There are three special names given to triangles that tell how
many sides (or angles) are equal.
There can be 3, 2 or no equal sides/angles:
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Acute Triangle
All angles are less than 90°
Right Triangle
Has a right angle (90°)
Obtuse Triangle
Has an angle more than 90°
What Type of Angle?
Triangles can also have names that tell you what
type of angle is inside:
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The Rhombus
A rhombus is a four-sided shape where all sides have equal
length.
Also opposite sides are parallel and opposite angles are equal.
Another interesting thing is that the diagonals
meet in the middle at a right angle.
In other words they "bisect" (cut in half) each other at right angles.
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The Parallelogram
A parallelogram has opposite sides parallel and equal in length.
Also opposite angles are equal (angles "a" are the same,
and angles "b" are the same).
NOTE: Squares, Rectangles and Rhombuses
are all Parallelograms!
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The Trapezoid
A trapezoid has a pair of opposite sides parallel.
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CIRCLE
The Radius is the distance from the center to the edge.
The Diameter starts at one side of the circle, goes through the
center and ends on the other side.
The Circumference is the distance around the edge of the circle.
And here is the really cool thing:
When you divide the circumference by the diameter you get
3.141592654... which is the number π (Pi)

Cube
It has 6 Faces
Each face has 4 edges, and is actually a square
It has 12 Edges
It has 8 Vertices (corner points)
and at each vertex 3 edges meet
Surface Area = 6 × (Edge Length)2
Volume = (Edge Length)3
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A cuboid is a box-shaped object.
It has six flat sides and all angles are right angles.
And all of its faces are rectangles.
The volume is found using the formula:
Volume = Length × Width × Height
And the surface area is found using the formula:
A = 2wl + 2lh + 2hw
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A pyramid is made by connecting a base to an apex
Pyramid
The Volume of a Pyramid =
1/3 × [Base Area] × Height
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Cone
•The pointy end of a cone is called the vertex or apex
•The flat part is the base
Surface Area of Base = π × r2
Volume = π × r2 × (h/3)
Surface Area of Side = π × r × √(r2+h2)
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The Volume of a prism is simply the area of one end times the length of the prism
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Triangular Pyramid
It has
4
Faces
· The 3 Side Faces are Triangles
· The Base is also a Triangle
It has 4 Vertices (corner points)
It has 6 Edges
It is also a Tetrahedron
And for reference:
Volume = 1/3 × [Base Area] × Height
Surface Area (when all side faces are the same):
= [Base Area] + 1/2 × Perimeter × [Side Length]
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CYLINDER
Volume of a Cylinder
Just multiply the area of the circle by the height of the cylinder:
Area of the circle: π × r2
Height: h
Volume = Area × Height = π × r2 × h
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SPHERE
All points on the surface are the same distance from
the center
Volume = (4/3) × π × r3
Surface Area = 4 × π × r2
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Math cps final

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