Narrator Akira receivesa prize at a science fair for having the most informative project. Her trophy is in the shapeof a square pyramid and is covered in shiny gold foil. So this is what her trophy looks like.
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How much gold foil did ittake to cover the trophy, including the bottom? And so they give us somedimensions and we want how much gold foil and it'sin inches squared so it's really going to be an area. So pause this video and seeif you can figure that out. How much gold foil did ittake to cover the trophy?
Alright now let's workthrough this together. And so essentially whatthey're asking is what is the surface area of this square pyramid. And we're doing to includethe base 'cause the surface area is how much, it'sthe area of the gold foil that is needed. Now, sometimes, some ofyou might be able to think about this just by looking at this figure, but just to make surewe don't miss any area, I'm gonna open up thissquare pyramid and think about it in two dimensions. So what we're gonna do isimagine if I were to unleash or if I were to cut the topand, let me do this in red, if I were to cut this edge, if I were to cut this edge, if I were to cut that edge, and that edge.
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So the edges that connectthe triangular sides and if I were to just open it all up, what would this look like? So if I were to open it all up? Well at the bottom youwould have your square base.
Let me color that in. So you have your square base. So let me draw that.
You have your square base,this is gonna be a rough drawing. And what are the dimensions there? It's three by three. We know this is a squarepyramid so the base, all the sides are the same. They give us one side, butthen this is three inches then this is gonna bethree inches, as well.
Let me color that samecolor just so we recognize that we're talking about this same base. And now if we open upthe triangular faces, what's it going to look like? Well this is going to look like this. This is a rough hand drawing,hopefully it makes sense. This is going to look like this. Each of these triangularfaces, they all have the exact same area. And the reason why I knowthat, they all have the same base, three, and theyall have the same height, six inches.
I'll draw that in a second. So they all look something like this. Just hand drawing it. And all of their heights,all of their height are six inches.
So this right over here is six inches. This over here is six inches. This over here is sixinches, and this over here is six inches.
So to figure out howmuch gold foil we need we're trying to figureout this surface area, which is really justgonna be the combined area of these figures. Well the area of thiscentral square is pretty easy to figure out. It's three inches by threeinches so it would be nine inches squared. Now what are the area of the triangles? Well we could figure outthe area of one of the triangles and then multiply by four, since there are four triangles. So the area of thistriangle right over here, it's going to be 1/2 times our base, which is three, times three, times our height, which is six. Let's see, one half times three times six, that's one half times 18which is equal to nine.
Nine square inches, ornine inches squared. So what's gonna be our total area? Well you have the areaof your square base plus you have the four sides, whicheach have an area of nine.
So I could write it out, Icould write four times nine or I could write nine- Do that black color. Or I would write nine plusnine plus nine plus nine. And just to remind ourselves,that right over there is the area of one triangular face. Triangular, triangular face. So this is all of the triangular faces. Triangular faces.
And of course we haveto add that to the area of our square base. So this is nine plus nine times four, you could do this as nine times five, which is going to be 45 square inches. Nine plus nine plus nineplus nine plus nine.
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The Quiz Press creates tests and quizzes, and distributes them in print, over the Web, for the iPod, or to other testing systems. Quizzes can include six different question types (Multiple Choice, Fill in the Blanks, Short Answer, True or False, Essay, and Cloze), and also allows for fully customizable titles. Web quizzes are delivered in Flash, so they are fun to use and cross-platform.
They can be published as stand-alone pages or embedded within other web content, and on any website. The quizzes can also be printed for conventional testing. The Quiz Press was designed to be easy to use from the ground up. Full Specifications What's new in version 2.5.12Version 2.5.12:. The splitter between the question list and the detailed question view now works again (broken in version 2.5.11)2.5.11 (Feb 29, 2012). The executable package is now 'OS X Mountain Lion' (10.8) compatible. Fixed the 'Help' Link.
Improved the tab ordering in Quiz Settings window. Various other improvements.2.5.10 (Dec 9, 2011). Exported GIFT files can now have more than 1 answer explanation specified. This version also includes other GIFT file format enhancements.GeneralPublisherPublisher web siteRelease DateMarch 01, 2012Date AddedFebruary 29, 2012Version2.5.12CategoryCategorySubcategoryOperating SystemsOperating SystemsWindows 2000/XP/2003/Vista/Server 2008/7Additional RequirementsNoneDownload InformationFile Size3.19MBFile Namequizpresswin.zipPopularityTotal Downloads468Downloads Last Week1PricingLicense ModelFree to tryLimitations5-question trialPrice$49.95.
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