oh [Music] welcome youtubers to another episode in my grammar hero series in today's video i want to review the 10 geometry formulas you must absolutely memorize and fully understand in order to pass both the armed services vocational aptitude battery that is the asvab as well as the pre-screening internet delivered computer adaptive test that is the pycat as a reminder on both the asvab and pycat you're not permitted to use a reference sheet and in my experience these are the 10 most important geometry formulas you must know in order to pass those tests in other words if you already know these 10 formulas you'll probably do pretty well on the test that said as we go through these formulas if you only know about four or five of them that means you need to spend a few extra weeks preparing for this test and thankfully enough all these formulas are very simple and easy to learn so with all that said let's get started with this knowledge check more specifically i'm gonna present you with a formula that you have to know at that point i want you to pause the video attempt to write out that formula and then resume playing the video to see if you in fact knew that formula so with all that being said let's get started with this knowledge check all right so uh the first formula i want to talk about is the area of a triangle if you would pause the video and attempt to write out that formula right now all right so finding the area of a triangle is pretty simple you should know that the formula to find the area of a triangle is equal to area equals one-half times the base of the triangle times the height of the triangle in other words the area of a triangle is one-half base times height and if you take a look at the figures to the left you can see that depending on the type of the triangle you're working with the height is either outside inside or far outside the triangle itself but that said all you have to know for the asvab and pi cat is that to find the area of a triangle you do area equals one-half base times height all right so the second most important formula that you need to know for the asvab and pi cat is the pythagorean theorem so again if you would pause the video and attempt to write out that formula right now right the formula for the pythagorean theorem is this it's a squared plus b squared equals c squared and additionally you have to know a few things about a b and c more specifically you have to know that a and b refer to the legs of a right triangle and c refers to the hypotenuse of a right triangle so in other words you can only use the pythagorean theorem when you're dealing with right triangles again a and b are in regard to the legs of the right triangle and c is in regard to the hypotenuse of a right triangle as it happens the hypotenuse is always very easy to identify in a right triangle it's always directly across from the right angle now another thing i want to say about the pythagorean theorem is this you have to understand that if you have at least two of these variables you can solve for the third variable in other words if you have a and b you can solve for c if you have b and c you can solve for a and if you have a and c you can solve for b so the next two formulas that you absolutely have to know for the asvab and pi cat are the area of a circle and the circumference of a circle so if you would pause the video and attempt to write those two formulas out as a matter of fact i'll give you a hint for circumference of a circle there are actually two formulas that you can use and you have to know both of them all right so with that said pause the video and see if you can write those out all right so in terms of finding the area of a circle you should know this to find the area of a circle it's going to be pi times the radius squared that is area of a circle is pi r squared where r is the radius of the circle and for pi on the asvab you're either going to use 3.14 to approximate pi or you're going to use the fraction 22 over 7 to approximate pi more often than not you're going to use 3.14 to approximate pi that said if you're doing especially well on the asvab they may make you approximate pi with 22 over 7. thankfully enough i have practice test videos where i use both of those interchangeably all right and in case you're wondering the radius of the circle is simply the distance from the center of the circle to the edge of the circle all right so that is the formula to find the area of a circle pi r squared uh let's talk about finding the circumference of a circle again here there are two formulas you need to know because it may show up either way on the test uh circumference of a circle c can be found simply by multiplying pi times the diameter of the circle or the circumference of the circle can be found by doing 2 times pi times the radius of the circle and again for pi you're going to either approximate it using 3.14 or 22 over 7. so you have to know these three formulas in regard to circles uh for the asvab and pi cat area's area of a circle is pi r squared circumference of a circle is pi times diameter or 2 pi r again i have videos where i go through the ins and outs of all three of those formulas all right so the next set of formulas you need to know for the asvab and pi cat are the perimeter of a square and the area of a square and let me just say this these are probably the easiest formulas to know and for that reason questions involving perimeter and area of squares tend to show up pretty frequently on the test that said to help you out i want to mention a few things squares have certain properties with which you should be familiar notably all the sides in squares are equal so that side's equal to that side that side's equal to that side and that side is equal to that side so if that side's s this side's s this side's s and of course this side is s to find the perimeter of any polygon you simply add up all of its sides so with those things in mind i try to write out the formula to find the perimeter and area of a square all right so finding the perimeter of a square is fairly simple and straightforward as i just mentioned to find the perimeter of a square you're simply going to add up all of its side so if you start here and go all the way around to get back to where you started that would be side plus side plus side plus side since squares of course have four sides the other formula you need to know is simply uh the simplified version of this this is s plus s plus s plus s in other words there are four s's there so if you know that perimeter of a square is s plus s plus s plus s which is the same thing as 4s you'll be good to go on the asvab all right as far as finding the area of a square goes that formula is pretty simple and straightforward it's area equals psi times side and of course you can simplify that to be area equal side squared so either those two formulas would work for finding the area of a square all right so uh the next set of formulas you have to know for the asvab is in regard to finding the perimeter of a rectangle as well as the area of a rectangle finding the perimeter of polygons excluding circles is fairly easy to find the perimeter of any polygon you simply add up all of its sides so with that said pause the video and see if you can write out these formulas all right so let's talk about finding the perimeter of a rectangle again we're simply going to add up all of its sides so if we start here we're going to go around and add all of these up so that's going to be width plus length plus width plus length now some people simplify this formula to be this what do we have here we have two w so that would be two w plus what do we have here we have two l's so that's two l's either of these formulas is correct if you know it either way you'll be fine on the asvab now there's only one formula to find the area of a rectangle and that is simply length times width all right so that is that one you do have to know how to find the perimeter and area of a rectangle for the asvab and picat alright so next to last you need to know how to find the area of a parallelogram this one's fairly simple uh so that said pause the video and see if you can write out that formula to find the area of a parallelogram you simply take the base of the parallelogram and you multiply by its height that is to say area of a parallelogram is base times height of course you can see the height is always inside the parallelogram now some of you are going to say well aren't you going to explain that in more depth i have videos on that already and i'll post links to those videos in the description of this one so finally you have to know how to find the volume of a rectangular prism and you just want to keep in mind that sometimes rectangular prisms are referred to as boxes thankfully enough this formula is pretty easy to remember so if you would pause the video and see if you can write out that formula all right so to find the volume of a rectangular prism or a box it's always going to be length times width times height you absolutely have to know that formula for the asvab and pi cat now that i've talked about the 10 most essential geometry formulas that you have to know for the asvab and pi cat let's talk about two more uh since these other two do show up from time to time on the asvab and pi cat that is let's talk about how you find the volume of a cylinder and uh before i ask you to write this formula out i want to say this the top of a cylinder is in the shape of a circle so if you can find the area of a circle then you can easily find the volume of a cylinder all right so that's it if you would pause the video and attempt to write this formula out all right so as i just mentioned uh if you know how to find the area of a circle you can find the volume of a cylinder very easily again this formula has two parts the first part of it is finding the area of one of these circular faces so how do you find the area of a circle that's simply pi r squared we've already talked about that formula in this video now to find the volume of a cylinder which is basically a circle that has been stretched out all we do is take the area of the face of the circle and multiply it by the height of the cylinder so the formula to find the volume of a cylinder is pi r squared times height that is right here we have the area of a circle times the height of these cylinder that is it again if you know how to find the area of a circle you can easily find the volume of a cylinder those two are very much interconnected all right so finally let's talk about one formula for algebra that shows up frequently on both the asvab and pi cat and that is in regard to finding the slope of a line all right so if you would pause the video and see if you can write this formula out all right so this formula is m where m refers to slope is equal to y2 minus y1 divided by x2 minus x1 and you might be saying to yourself where do you get x1 y1 x2 y2 from well you get those values from the two ordered pairs that you're given and as you can see over here we have one point notably x1 y1 and we have this second point that will be x2 y2 so in order to plug in these values you have to be given two points and of course i have a video on finding the slope of the line if you need more practice with that so speaking of practice i want to say this while it's important to memorize the formulas we just went through in order to be successful on the asvab and picat you also have to fully understand how to manipulate those formulas as well so for that reason you do have to practice using those formulas not surprisingly i've thought of that already and for that reason i put together a geometry review playlist for the asvab and pi cat if you go through this geometry review playlist from start to finish you will be exceptionally well prepared for both the asvab and pycat as a matter of fact if you work through the 10 videos in this playlist you'll see that there are about 10 practice test questions for each of the formulas we just went through so again i will put a link to this playlist in the description of this video if you struggled with anything in this video please go through this playlist it will prepare you for the test all right so that is it for this video as always i hope you found it helpful and as usual you're more than welcome to leave feedback in the comments section below as i said at the start of this video you absolutely have to memorize and fully understand these 10 geometry formulas in order to be successful on the asvab and pycats for that reason please check out my geometry review playlist if you need to even if you know these formulas fairly well it's a good idea to check that playlist out just to make sure that you fully understand these formulas with all that being said there are two things you can do to help my channel out you can one subscribe to it if you like my content and two you can share links to my videos including this video on social media including on facebook and twitter and on that note i'm gonna go ahead and catch you loose [Music]