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Squares: Definition and Properties

Squares: Definition and Properties
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  • 0:07 Squares
  • 1:44 Perimeter
  • 3:01 Area
  • 4:11 In the Real World
  • 5:06 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Squares can be found in many places in the real world. Watch this video lesson to see how useful they can be and also to learn how to find the perimeter and area of a square.

Squares

How do you know when you are looking at a square? You are looking at a square when you see a four-sided figure whose sides are all the same length and whose angles are all right angles measuring 90 degrees.

Squares are also flat shapes, meaning they can be drawn on a flat piece of paper. Try drawing one right now. Pause this video, and give it a try.

Do you see the little squares and dashes I've drawn below?

Each corner in a square is 90 degrees, and each side is the same length.
squares and dashes drawn for squares

The little squares are there to show that each corner is a right angle measuring 90 degrees. Each little dash shows that every side with the dash is the same length. Those are the two major properties of squares. They also define a square and make it different from all other shapes.

A square does have a couple other properties. For one, because of the right angles, the opposite sides of the square are parallel. If you draw out the lines for the top side and the bottom side, you will see that the lines will never meet or intersect with each other. Second, because of the strict side and angle requirements, squares also fall under the category of quadrilaterals (four-sided shapes), regular polygons (a shape whose sides are all the same length), rectangles (four-sided shapes whose angles are all right angles), and rhombuses (four-sided shapes whose sides are all the same length). Pretty cool, huh?

There are two different calculations that are done on squares. They are the perimeter and the area. Let's talk about them now.

Perimeter

Generally speaking, the perimeter is the distance around a shape. I like to think of a perimeter in terms of walking around the shape. Say, for example, you drew a giant square using chalk on the ground. You would be able to find the perimeter by starting at one corner and measuring the distance it takes you to walk all around the edge of the square until you returned to the corner where you started. Of course, many of the squares you will be dealing with will be much smaller, and you won't be able to walk around them. But, you know what? You can thank the mathematicians, because we have a handy-dandy formula we can use to find our perimeter for a square.

It is perimeter = 4s, where the s stands for the length of each side. Yes, all we have to do is to multiply the length of one of the sides by 4 to find our perimeter. It's easy to remember if you think of the definition of a square. A square has four equal sides, so 4 times a side gives you the total distance around the square. Easy, don't you think?

If I had a square whose length of each side is 2 inches, the perimeter will then be 2*4, or 8 inches.

Area

The next calculation is that of area, or the amount of space inside the shape. I visualize area in a similar way to perimeter. If you return to the giant square that you drew on the ground, the area is the amount of space you have to walk around inside the square. Also, for area, the mathematicians have an easy formula we can use.

It is area = s^2. The s is the length of a side of the square. What we are doing is multiplying how wide the square is by how long the square is. Because they are both the same length, we end up squaring just one side to find our answer.

Going back to the square with the 2-inch sides, the area for this square is 2^2, or 2*2, or 4 inches squared. Remember, because you are multiplying two units together, your units are also squared. In this case, we are multiplying inches by inches, so our answer will be in inches squared.

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