Math 252 Measurement
Pythagorean Theorem
A^2+B^2=C^2
"C" is the longest side across from the right angle, "A" and "B" are the other two sides of the triangle that make up the sides of the right angle
Only applies to right triangles
Measurement is Not Necessarily the Distance From Zero
Remember that when teaching mesaurement, it is important the remind kids that measurement is the distance between the start and the finish of the object rather than where the object ends in relation to zero on a ruler
Remember the video Christina showed in class of her son looking at the two bear icons lined up against the rulers?
It is important to remember that even though surface area deals with 3D objects, it is still measured in units squared because you are only measuring the 2 dimensions that create the faces of the object (the outside surfaces), and not any of the inside of the object
I personally think it is easiest to find surface area by dividing the polyhedron up into the individual polygons that make up the faces of the polyhedron and finding the areaof each polygon then adding them together
Slant Height vs. Perpendicular Height
Perpendicular Height: this height is the length of a straight line drawn from the top of the object down to where it intersects perpendicularlly with the base
Slant Height: this is the height typically seen in rhombi or pyramids that instead of measuring the height from the very top of the object straight down to the bottom measures a slanted edge
Formulas
Surface Area
Cone: (pi)r^2+(pi)rs
Pyramid: B+1/2ps
Prism and Cylinder: 2B+ph
Pyramid/Cone: 1/3(Bh)
Prism/Cylinder: Bh
Area
Trapezoid: 1/2(a+b)h
Triangle: 1/2(bh)
Parallelogram: bh
Rectangle: bh
Circle: (pi)r^2
Circumference of a Circle: 2x(pi)xr
Area Formulas
Trapezoids: (Length of base 1+ Length of Base 2)/2 then x perpendicular height
Triangles: (Height from Apex to Base x Length of Base)/2
Quadrilaterals: Perpendicular Height x Length
Volume
For prisms it is helpful to think of the volume as the area of the base (B) simply stacked on top of itselfenough times to reach the height of the prism
Cones and pyramids are similar in this aspect but it is almost like someone stacked the base on top of itself to reach the height and then cut pieces out. In fact, it is like they cut out two thirds of the original prism or cylindar
For this reason, the volume formula for cones and pyramids is Bh/3
Cubes/Rectangular Prisms: Length x Width (this gives you the area of the base) x Height
Unit/Labeling is important
It is crucial to identify which unit you are measuring in and what part of the object you are measuring in order for others to be able to duplicate or understand your results
Volume requires cubed units because when you measure volume you are measuring in three dimensions (height, depth, and width)
Area and Surface Area reguire squared units because when you measure area you are measuring in two different dimensions (length and width)
