Measurement: Length, Area, & Volume

The measurement process is an essential process in knowing the size of something. This process has a very long history in comparing what you have to a special size. Measurements have long been practices by comparing items to parts of your body.

(i) Choose the property, or attribute (such as length, area, volume, capacity, temerature, time, or weight), of an object or even that is to be measured. (ii) Select an appropriate unit of measurement. (iii) Use a measurement device to "cover", "fill", "time", or otherwise provide a comparison of the object with the unit. (iv) Express the measurement as the number of units used.

InchFootYardRodFurlong ("furrow long" has to do with Agriculture)Mile

Square InchSquare FootSquare YardAcreSquare Mile

Cubic InchCubic FootCubic Yard

TeaspoonTablespoonFluid OunceCupQuartGallon

The metric system of measurement originated in France around 1789. In many efforts to get the U.S. to use the system they failed (That is why we have our own system of measurements), but Great Britain, Canada, Australia, and New Zealand did adopt this system. There is a huge advantage to using the Metric System, as it is easy to campare due to the use of the powers of ten. Instead of going from inches to feet by adding a bunch of numbers, you move a decimal. EX: 1234 km to 1.234 m

Kilo (10^3)Hecto (10^2)Deka/Deca (10^1)Basic unit (10^0)Deci (10^-1)Centi (10^-2)Milli (10^-3)Micro (10^-6)

The sum of the area of the squares on the legs of a right triangle is equal to the area of the square on the hypotenuse.

Let R be a region and assume that a unit of area is chosen. The number of units required to cover a region in the plane without overlap is the AREA of the region R.

If a region is bounded by a simple closed curve, then the PERIMETER of the region is the length of the curve. More generally, the PERIMETER of a region is the length of its boundry.

Volume is the amount of space that is enclosed inside a boundry. Finding this is important and useful if you want to find how much of something can be held within a boundry.

The volume of a rectangular box has the formula of: V=lwh

The volume of a right prism or a right cylinder formula is:V= BhThe B= to the area of the base

The the volume of a general prism formula is:V=Bh

The volume of a pyramid or a cone formula is:V= 1/3Bh

The volume of a sphere formula is:V= 4/3(pi)r^3This formula is usually the most confusing one to do. On your calculator you can use either the pi symbol or you can multiply it by 3.14. The "r" stand for radius, which is half of the diameter.

SA= 2B + phh represents the height of the prism or cylinderp represents the perimeter of each base

SA= B + 1/2ps s represents the slant height, since triangles do not have a line straight up and down. p represents the perimeter of the triangle

SA= (pi)r^2 + (pi)rs s represents the slant heightr represents the radius, which is half of the diameter

S= 4(pi)r^2 r represents radius, which is half of the diameter

If R and S are regions in the plane that have the same size and shape, then they are CONGRUENT and we use the ≅ symbol to write R≅S.

If region R is congruent to region S, then the two regions have the same area:area(R)=area(S)

If a region R is dissected into nonoverlapping subregions A, B, ..., F, then the area of R is the sum of the areas of the subregions:area(R)= area(A) + area(B) + ... + area(F)

Let a triangle have sides of length a, b, and c. If a^2 + b^2= c^2, then the triangle is a right triangle and the angle opposite the side of length c is the right angle.