Author Archives: hangtime
Sector Area Word Problems
By popular demand, a separate video of word problems! Naturally there are a few pizza problems (we are talking about sectors, after all), but we'll also get into percentages and pie charts, which seem to be the only place you come across sectors after geometry class is over (other than when you're eating pizza).
Areas of Circle Sectors
Even for sectors with crazy angle measures, I find that always thinking of sectors as slices of pizza is really the best way to make sene of what is otherwise a confusing topic.
Basic Circle Area Problems
This video shows you how to work the most common types of circle area problems, and tricks for avoiding errors. The easier ones are when the problem provides a radius and asks for area. In the harder area problems you are given something other than radius, such as circumference or diameter, or you are asked to work backwards from area to find radius or diameter.
Is Pi really 22-7?
Rumor or innuendo? Fact or fiction? Truth or dare? Rationally repeating decimal or... I could go on but won't. If your teacher or friend has told you that pi is 22/7, this video may be for you. If this is the first you're hearing that pi is 22/7, no need to watch.
This chapter is super-important if you're ever planning on taking the SAT or another tough standardized test. You won't see sectors too much after Geometry class, but circles and circle-ish regions, especially "shaded regions" involving circles and triangles, are favorite topics for test-makers everywhere!
How to Find Apothems of Regular Polygons
When you learn to find the area of regular polygons, you are given a formula (A=½ap) that uses something called the "apothem". This video explains how to find the apothem using either SohCahToa or special triangles.
Finding Area of Regular Polygons
This video explains how to find area of polygons using the apothem formula: A=½ap. It also shows you how to find polygon area in a way that you'll actually remember by the time your final rolls around.
The first video in this chapter covers what an apothem is and how to find it. The second shows you how to use the apothem formula to find the area of regular polygons such as pentagons, hexagons, octagons, etc., and it also explains how to find the area of regular polygons a better way.
Proof of Rhombus & Kite Area Formula
You don't need to watch this video unless you have a seriously hard teacher. Or you just don't get where the heck that funky A = ½ d1d2 formula came from.
Area of Rhombi (Rhombuses)
Are rhombuses kites or parallelograms? That is the question. When resting on one side, rhombi look like parallelograms, and you should probably use A=bh to find the area. On the other hand, when a rhombus is vertical, it looks more like a kite and you may prefer to use A = ½ d1d2. Whichever method you prefer, I'll show you how to use the other one as well, since teachers have a habit of forcing you to do what you don't like.
Area of Kites
Kites don't look much like rhombuses (unless you rotate them so they're sitting on one side), yet the area formula is the same, and so are the tricks. Just like with rhombi, in this video I'll use SohCahToa and special triangles to work each kite area problem two ways: one time using triangles, and a second time using the area you probably won't remember when really need it, A = ½ d1d2.
Rhombuses unfortunately use the same area formula as kites -- A = ½ d1d2. "Unfortunate" because you won't remember that formula a year or even 3 months from now when you need it on a big test! So in this chapter, whenever I work an area problem I'll also show you how to work it using parallelograms or triangles, since that's how you'll remember to do it long after the diagonals formula is lone gone from your mind.
Parallelogram & Trapezoid Area Word Problems
Yeah, word problems! What happens to the area of a rectangle when you "tip it over" into a parallelogram? How can one use triangles to approximate the area of a trapezoidal airplane wing? What to do when you are given the area of a trapezoid and have to then solve for x? Why am I asking all these rhetorical questions?
Areas of Parallelograms & Trapezoids with SohCahToa
When you're supposed to find the area of a parallelogram or trapezoid and they give you an angle as well as a side, chances are you're supposed to use SohCahToa (trig). Sometimes you have to use special triangles even if no angles are given, because you're "supposed to know" the special triangle ratios! Wow. This video shows you what to look for.
Areas of Parallelograms & Trapezoids on X-Y Coordinate Axes
This is one of those trick questions that every teacher uses: they think that if they draw a figure on a grid instead of labeling the sides, their students will become confused by all the square roots of the distance formula. And they are right. But you should actually look forward to these problems, because if you do them right, 99% of the time you won't even need the distance formula!
Areas of Trapezoids
This video covers basic trapezoids, of course, but more importantly it covers the problems that aren't quite so plug-and-chug. Isosceles trapezoids, for example, are trick questions used by most teachers because they force you to be able to split the trapezoid into right triangles that require SohCahToa or special triangles to find the height. Another common trick: funky trapezoids turned up on their end so that they don't even look like trapezoids.
Area of Parallelograms
The area formula for parallelograms (or parallelagrams if you misspell it) -- A = bh -- is pretty easy. But this video also covers the most common tricks your teacher can throw at you, like making you use SohCahToa and special triangles to solve for area. Also explained are how to make rectangles out of parallelograms, which sounds silly but is kind of the basis of most area formulas.
Examples and word problems using parallelograms (parallelagrams sp) and trapezoids.
Triangle Area Word Problemse
Yay, word problems! This batch all involve triangles, with a couple practical ones and a couple conceptual ones.