# Rectangle: Types, Properties & Formulas

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• 0:00 What Is A Rectangle?
• 0:40 What Makes A Rectangle…
• 1:45 Special Types Of Rectangles
• 2:50 Using Rectangles In…
• 4:25 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.

Did you know that a special type of rectangle can be found in the Mona Lisa painting? Learn what this type is. Also learn what makes a rectangle a rectangle, and how to make calculations with them.

### 1What Is a Rectangle?

Simply put, a rectangle is any four-sided figure that also has four right angles (90 degree angles). Look around you and you can see them all around you in the world. Most likely, the room you're in is some form of a rectangle or a combination of rectangles. It's a simple shape that is easy to work with.

You probably also drew a rectangle when you first drew a house as a kid. What shapes are most doors that you see? Aren't they rectangles? What about windows? Don't they all have four sides and four right angles?

In addition to having four sides and four 90-degree angles, there are some other properties that all rectangles must possess.

## What Makes a Rectangle a Rectangle?

There are several things that make rectangles special and set them apart from other shapes. The first two have already been mentioned, but here they are again along with some more:

• It must have four sides.
• All four angles must be 90 degree right angles.
• A rectangle is a special case of a parallelogram; its opposite sides are parallel. Like a parallelogram, the opposite sides are equal in length to each other. There are two pairs of opposite sides, and each pair could have a different length, but each pair's sides will be equal to each other.
• The diagonals of a rectangle are equal in length to each other and they bisect each other at their point of intersection. When you draw a line that cuts the rectangle into two triangles and then do it again to the other two corners, these two lines will be equal in length to each other. These two lines also cross at exactly the midpoints of each. So, each diagonal cuts the other in half.

All of the above must be met for a shape to be considered a rectangle. Even with these requirements, there are rectangles that fall under their own very special types.

## Special Types of Rectangles

There are two special types of rectangles that have even stricter requirements than just rectangles.

• The first is a square. A square is a rectangle with the added requirement that all sides are equal in length. You can fit a square in a rectangle whose width is the same as the width of the square, given that the length of the rectangle is longer than the width.
• The second is the Fibonacci rectangle. This special rectangle adds the requirement that the length to width ratio be 1.618. In other words, the length is 1.618 times longer than the width. So, if the width is 2, then the length is 2 times 1.618, or 3.236.

This special type of rectangle is also called the golden rectangle because its ratio is the golden ratio of 1.618. Looking at the Mona Lisa painting, mathematicians have noticed that the rectangle that goes from her head to her right hand and left elbow has the proportions of the golden rectangle.

## Using Rectangles in the Real World

When using rectangles in the real world to solve problems, there are only a few formulas to keep in mind. They are for the area, perimeter, and diagonals of the rectangle.

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