Measurement Project Math 252.02
Surface Area
If two figures of similar lengths depending on their shape the surface area will be similar or different
B-area of base
p-perimeter of shape
h- height of shape
r- radius of shape
s-length of the side (slant)
Sphere
4 (3.14) (r^2)
(3.14)(r^2)+(3.14)(r)(s)
B+1/2 ps
2B+ph
2 B+ph
The total area covered by the net of a polyhedron
Geometric Figures
Angles: the space between two intersecting lines. Angles are measured in degrees.
Parallel angles: two straight angles that will not intersect; they have no parts in common.
Straight Angle: 180 degrees line, basically just a straight line.
Exterior Angle: the angles that are outside of the polygon; the line of one side of the polygon is extended and from that extension to the corresponding side is the angle measure.
Interior Angles: the angles that are inside the polygon
Corresponding Angles: two angles that are in the same relative position on two different lines intersecting a straight line.
Vertical Angles: two angles that are opposite of each other made by two intersecting lines.
Congruent Angles: two angles that are the same size and shape, and mirror each other.
Complimentary Angles: two angles that, when added together add up to 90 degrees. Usually when one angle measure is known, denoted as x, an equation to find the complimentary angle is 90 - x.
Supplementary Angles: two angles that, when added together, add up to 180 degrees. Usually when one angle measure is known, denoted as x, an equation to find the supplementary angle is 180 - x.
The Sum of Interior Angles: the sum of the measures of the interior angles of any convex polygon with n sides is (n-2) X 180
Classification of Angles
Obtuse Angle: two lines that when intersect, measure to more than 90 degrees.
Acute Angle: two lines that when intersect, measure to less than 90 degrees
Right Angle: two lines that are perpendicular to one another; 90 degrees.
Three-deminsional Polygons
Sphere: A 3-dimensional object shaped like a ball. Every point on the surface is the same distance from the center.
http://www.mathsisfun.com/definitions/sphere.html
Non-circular cone: a gone with a non-circular base and one lateral side to an apex.
Circular cone: a cone with a circular base and one lateral side to an apex.
Cylinder: parallel circular bases with one lateral side.
Oblique cylinder: the lateral side is at a n degree angle bases.
Right cylinder: the lateral side is at a 90 degree angle to the bases.
Pyramid: a base with triangular sides that meet at an apex.
Oblique pyramid: the apex of the pyramid makes a n-degree angle to the base.
Right pyramid: the apex of the pyramid makes a 90 degree angle to the base. The lateral faces are also all congruent and isosceles.
Prism: two congruent faces on parallel planes bound together together by parallelograms.
Right prism: the sides are at a right angle to the base and are always rectangles.
Oblique Prism: the sides are at an n-degrees angle to the base.
Two-Dimensional Polygons
Regular Polygons: polygons that are equilateral and equiangular. Need both parts.
Quadrilaterals: a polygon with four sides
Kite: a quadilateral with no lines that are paralell to one another.
Rhombus: a parallelogram that has congruent sides and angles.
Square: a rhombus that has congruent sides of any length and congruent angles equal 90 degrees. (a square can be a rectangle but a rectangle can not be a square)
Trapezoid: a quadilateral with two lines that are paralell to one another.
Parallelogram: a trapezoid where all opposite sides are parallel.
Rectangle: a parallelogram that has congruent angles of 90 degrees.
Isosceles trapezoid: a trapezoid with two sides that are the same length
Triangles: a polygon with three sides
Equilateral triangle: a triangle where all three sides are the same lenth.
Isosceles triangle: a triangle where two of the three sides are the same length.
Scalene triangle: a triangle where all three sides are different lengths.
Angles of a triangle: all the angles in the triangle must equal 180 degrees.
Acute triangle:a triangle where all it's angles are less than 90 degrees.
Obtuse triangle: a triangle with one angle that is more than 90 degrees and the remaining two angles are less than 90 degrees.
Right triangle: a triangle with one 90 degree angle.
Circles: A 2-dimensional shape made by drawing a curve that is always the same distance from a center.
http://www.mathsisfun.com/definitions/circle.html
Circumference: the length around the circle, similar to a perimeter.
Diameter: the central distance from one end of the circle to the other, in any direction.
Radius: half of the diameter.
Pythagorean Theorem
Is it a Right Triangle?: You can determine if a triangle is Right by the Pythagorean Theorem. I.E. finding C.
When Finding C: First square both the lengths of sides A & B. Then add the two lengths together. If C is given, square C. If the lengths on each side of are equal it is a right triangle. If C is not given, Square root both the side lengths and C (so it will be a plain letter). This will give you the lenghth of C.
When Finding A or B: First square both the length for C and the given side, either A or B. Minus the length of the given side over the equal sign, subtract from C. Square root both the missing side, A or B, to make a plan letter. Square root the length you found with the given side and C. That'll give you the missing side length
Shorthand notation: A^2 + B^2 = C^2
Christina: Mindomom wouldnt let my type the 2s as exponents
Formula: A (squared) + B (squared) = C (squared)
Where A & B are the shorter sides and C is the hypothenuse
Volume
The amount of space a substance or oject occupies
Formulas
B- area of base
h- height of shape
r- radius of shape
Spere
4/3 (3.14) (r^3)
Cone
(1/3) Bh
Pyramid
(1/3)Bh
Cylinder
Prism
Bh
Area & Perimeter
Definitons
Circumfrance- The length around a circle
Radius- The length of half of the Diameter
Diameter- The length across a circle
Perimeter- The distance around a figure
Area- The measurement of a surface of a figure
Perimeter of a Curved Figure
Shorthand Notation:
P = (3.14)D
Where D is the Diameter
P = 2(3.14)R
Formula:
P = Pie X Diameter
P = Two X Pie X Radius
Perimeter of common Polygons
Shorthand Notation: P = N X S
Formula: The Number of sides X the length of one Side
Area of a Curved Figure
Area of a Circle
Shorthand Notation: A = (3.14)R2
Where R is the Radius
Formula: A = Pie (3.14) X Radius squared
Area of common Polygons
Height
In finding Area, the Height is not always a side, it can be the altitude depending on the shape. It must be straight.
Area of a Trapezoid
Shorthand Notation: (1/2) X H(B1 + B2)
Formula: A = Half X Height(Base 1 + Base 2)
Area of a Triangle
Shorthand Notation: (1/2) X (BH)
H is the altitude
Formula: A = Half X Base X Height
Area of a Parallelogram
Shorthand Notation: B X H
H is the Height
Formula: A = Base X Height
Area of a Rectangle
Shorthand Notation: L X W
Formula: A = Length X Width
