Measurement Project Math 252.02

Area of common Polygons

Area of a Rectangle

Formula: A = Length X Width

Shorthand Notation: L X W

Area of a Parallelogram

Formula: A = Base X Height

Shorthand Notation: B X H

H is the Height

Area of a Triangle

Formula: A = Half X Base X Height

Shorthand Notation: (1/2) X (BH)

H is the altitude

Area of a Trapezoid

Formula: A = Half X Height(Base 1 + Base 2)

Shorthand Notation: (1/2) X H(B1 + B2)

H is the altitude

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 Curved Figure

Area of a Circle

Formula: A = Pie (3.14) X Radius squared

Shorthand Notation: A = (3.14)R2

Where R is the Radius

Perimeter of common Polygons

Formula: The Number of sides X the length of one Side

Shorthand Notation: P = N X S

Perimeter of a Curved Figure

Formula:

P = Two X Pie X Radius

P = Pie X Diameter

Shorthand Notation:

P = 2(3.14)R

Where R is the Radius

P = (3.14)D

Where D is the Diameter

Definitons

Area- The measurement of a surface of a figure

Perimeter- The distance around a figure

Circumfrance- The length around a circle

Diameter- The length across a circle

Radius- The length of half of the Diameter

Formulas

Prism

Bh

Cylinder

Bh

Pyramid

(1/3)Bh

Cone

(1/3) Bh

Spere

4/3 (3.14) (r^3)

B- area of base
h- height of shape
r- radius of shape

The amount of space a substance or oject occupies

Formula: A (squared) + B (squared) = C (squared)

Where A & B are the shorter sides and C is the hypothenuse

Shorthand notation: A^2 + B^2 = C^2

Christina: Mindomom wouldnt let my type the 2s as exponents

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

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.

Two-Dimensional Polygons

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

Diameter: the central distance from one end of the circle to the other, in any direction.

Radius: half of the diameter.

Circumference: the length around the circle, similar to a perimeter.

Triangles: a polygon with three sides

Angles of a triangle: all the angles in the triangle must equal 180 degrees.

Right triangle: a triangle with one 90 degree angle.

Obtuse triangle: a triangle with one angle that is more than 90 degrees and the remaining two angles are less than 90 degrees.

Acute triangle:a triangle where all it's angles are less than 90 degrees.

Scalene triangle: a triangle where all three sides are different lengths.

Isosceles triangle: a triangle where two of the three sides are the same length.

Equilateral triangle: a triangle where all three sides are the same lenth.

Quadrilaterals: a polygon with four sides

Trapezoid: a quadilateral with two lines that are paralell to one another.

Isosceles trapezoid: a trapezoid with two sides that are the same length

Parallelogram: a trapezoid where all opposite sides are parallel.

Rectangle: a parallelogram that has congruent angles of 90 degrees.

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)

Regular Polygons: polygons that are equilateral and equiangular. Need both parts.

Three-deminsional Polygons

Prism: two congruent faces on parallel planes bound together together by parallelograms.

Oblique Prism: the sides are at an n-degrees angle to the base.

Right prism: the sides are at a right angle to the base and are always rectangles.

Pyramid: a base with triangular sides that meet at an apex.

Right pyramid: the apex of the pyramid makes a 90 degree angle to the base. The lateral faces are also all congruent and isosceles.

Oblique pyramid: the apex of the pyramid makes a n-degree angle to the base.

Cylinder: parallel circular bases with one lateral side.

Right cylinder: the lateral side is at a 90 degree angle to the bases.

Oblique cylinder: the lateral side is at a n degree angle bases.

Cone

Circular cone: a cone with a circular base and one lateral side to an apex.

Non-circular cone: a gone with a non-circular base and one lateral side to an apex.

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

Angles: the space between two intersecting lines. Angles are measured in degrees.

Classification of Angles

Right Angle: two lines that are perpendicular to one another; 90 degrees.

Acute Angle: two lines that when intersect, measure to less than 90 degrees

Obtuse Angle: two lines that when intersect, measure to more than 90 degrees.

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

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.

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.

Congruent Angles: two angles that are the same size and shape, and mirror each other.

Vertical Angles: two angles that are opposite of each other made by two intersecting lines.

Corresponding Angles: two angles that are in the same relative position on two different lines intersecting a straight line.

Interior Angles: the angles that are inside the polygon

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.

Straight Angle: 180 degrees line, basically just a straight line.

Parallel angles: two straight angles that will not intersect; they have no parts in common.

The total area covered by the net of a polyhedron

Formulas

Prism

2 B+ph

Cylinder

2B+ph

Pyramid

B+1/2 ps

Cone

(3.14)(r^2)+(3.14)(r)(s)

Sphere

4 (3.14) (r^2)

B-area of base
p-perimeter of shape
h- height of shape
r- radius of shape
s-length of the side (slant)

If two figures of similar lengths depending on their shape the surface area will be similar or different