Rachel
About

Khan Academy on a Stick

Geometry

Perimeter and area of triangles

You first learned about perimeter and area when you were in grade school. In this tutorial, we will revisit those ideas with a more mathy lens. We will use our prior knowledge of congruence to really start to prove some neat (and useful) results (including some that will be useful in our study of similarity).

Triangle inequality theorem

The triangle inequality theorem is, on some level, kind of simple. But, as you'll see as you go into high level mathematics, it is often used in fancy proofs. This tutorial introduces you to what it is and gives you some practice understanding the constraints on the dimensions of a triangle.

Koch snowflake fractal

Named after Helge von Koch, the Koch snowflake is one of the first fractals to be discovered. It is created by adding smaller and smaller equilateral bumps to an existing equilateral triangle. Quite amazingly, it produces a figure of infinite perimeter and finite area!

Heron's formula

Named after Heron of Alexandria, Heron's formula is a power (but often overlooked) method for finding the area of ANY triangle. In this tutorial we will explain how to use it and then prove it!

  • Circles: radius, diameter, circumference and Pi

    A circle is at the foundation of geometry and how its parts relate to each other is both completely logical and a wonder.

  • Labeling parts of a circle

    Radius, diameter, center, and circumference--all are parts of a circle. Let's go through each and make sure we understand how they are defined.

  • Area of a circle

    In this example, we solve for the area of a circle when given the diameter. If you recall, the diameter is the length of a line that runs across the circle and through the center.

Circumference and area of circles

Circles are everywhere. How can we measure how big they are? Well, we could think about the distance around the circle (circumference). Another option would be to think about how much space it takes up on our paper (area). Have fun!

  • Quadrilateral overview

    "Quad" means "four" and "lateral" means "line." A quadrilateral is literally a shape with four sides (lines) and four angles. Let's learn the difference between concave and convex quadrilaterals as well as trapezoids, parallelograms, and rhombi.

  • Quadrilateral properties

    How about this: we are given a 4-sided shape and asked to determine whether its properties qualify it to be called a quadrilateral (or category of quadrilaterals). Check it out.

  • Area of a parallelogram

    Guess what's interesting about the opposite sides of a parallelogram? That's right....there are parallel! Let's find the area--base times height

  • Area of a trapezoid

    A trapezoid is a cousin of the parallelogram. However, in trapezoid only two of the opposing sides are parallel to each other. Here's we explain how to find its area.

  • Area of a kite

    Who doesn't like kites? If you were going to make your own out of a piece of cloth, then knowing the area of the kite would be helpful, right? Let's see how it's done.

  • Perimeter of a parallelogram

  • Perimeter and area of a non-standard polygon

    Perimeter and Area of a Non-Standard Polygon

Perimeter and area of non-standard shapes

Not everything in the world is a rectangle, circle or triangle. In this tutorial, we give you practice at finding the perimeters and areas of these less-than-standard shapes!

Volume and surface area

Tired of perimeter and area and now want to measure 3-D space-take-upness. Well you've found the right tutorial. Enjoy!

Cross sections of 3D objects