Study Guide

Area Introduction

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Area Introduction

For as long as you can remember, your parents have always been free spirits. Actually, your friends prefer to call them hippies, but you've been raised to dislike societal labels. And honestly, do three Grateful Dead posters in the living room make you a hippie?

Although to be fair, they might have a point. After all, your first rattle had peace signs on it and your baby blanket was neither blue nor pink but tie-dye. Plus, it gets tiring to explain to everyone why you call your parents Wildflower and River instead of Mom and Dad.

So it only makes sense that after studying hours upon hours for your geometry test, your parents encourage you to unleash. "You've studied enough," they tell you. "And we know you'll do fine on that test tomorrow. Tonight, you can run wild. Be free. Paint the town red!"

You've already bought 50 gallons of red (though actually, it's called "Blissful Burgundy") paint before your friends tell you that painting the town red is just an expression. How were you supposed to know that? You've taken your parents literally ever since they stood on a street corner with a sign that said "Free Love" and gave hugs and kisses to passersby, free of charge.

With 50 gallons of Blissful Burgundy, what else can you do except go through with it? Time to paint the town red. Literally.

The thing is, you've been studying so much geometry that all you can do is think about how much flat surface you'll have to cover with this red paint. In your head, you begin to calculate all the areas of the walls, the roads, the streetlamps—all the 2D surfaces that will soon be the color of Blissful Burgundy.

Since geometry is all about mathematically understanding the world around us, it makes sense that it's everywhere we look. Even though our world is in a minimum of three dimensions (some might argue four, five, or even an infinite number of them), our vision is in two dimensions. In fact, there are many aspects of the second dimension that we can apply to the real world.

Whether you like it or not, the two-dimensional space known as area is one of those concepts that's quite literally everywhere. Much like Blissful Burgundy is soon to be. Now get out there and make Wildflower and River proud.

Area Resources


Area 51
When we said that area is applicable to the real world, we meant outer space as well. Read up about the most famous place with the word "area" right in its name.


Area, à la Shmoop
A quick recap of the basic concept of area, along with an example of how to calculate the area of a rectangle. Enjoy your trip to the second dimension. Bring us back a souvenir.

Going 'Round In Circles
Not only do they sing, they dance! Good thing they don't explain every geometry concept, or else we would be out of a job.

World Freehand Circle Drawing Champion
This guy is the Michael Jordan of drawing circles. If only he concluded with the epic Darth Vader quote, "The circle is now complete." (Insert obnoxiously heavy breathing here.)

Perimeter & Area Song
Confused about the difference between area and perimeter? Learn this song and be confused no longer. Then, try out for The Voice.

Games & Tools

Pyramid Panic
Do you know why the pyramids are the only ancient wonder still standing? It's because the Egyptians were so good at math. Test your math chops in this fun game. Don't get too wrapped up if you lose. #mummyjokes

Perimeter and Area
Here's a fun visual click-through discussing area and perimeter. Isn't it everything you wanted to know about area and perimeter? If not, that just means you're intellectually curious, and we appreciate that about you.

Area Tool
This is a nifty tool that calculates the area of trapezoids, parallelograms, and triangles in real-time. Who knew clicking and dragging could be so educational?

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