The Pythagorean theorum, maybe more than once. So with that in mind, I encourage you to pause the video and see It's perpendicular to the top of the rectangular prism. Is that this red line, that's one unit long, it is perpendicular, it is perpendicular to this entire plane. And so I encourage you to pause this video and try to think about it on your own. What is that length? And we will call that, These edges right over here? So either that one, or But our goal here, our goal here, is to figure out what is the length? What is the length of one of And this hasn't beenĭrawn completely to scale, and kind of the perspective Of its base right over here, and you go to the top, this height right over here is one unit. And then on top of that, on top of that, we have what you couldĬall a right pyramid, where the height of this right pyramid, so if you start at the center Guess we could say tall, four units wide, and then four units long.

That rectangular prism, it's three units I So we have an interesting shape right over here. Six is not a perfect square, so we leave our solution as *sqrt(6)*. When sqrt(5) is squared, the sqrt and the square cancel out, so 5. Great! Now we can plug the base and the height into the equation for the lateral edge. So the base of our final triangle, b, is sqrt(5). So sqrt(5) is the distance between the start of A and the start of the lateral edge.

To calculate the distance from the start of a to the start of the lateral edge, all we need to do is find the hypotenuse of the right triangle. If you draw it out, a point halfway along the edge of the rectangle, the start of a, and the corner where the lateral edge begins forms a right triangle.

What we're looking for is the distance from the center of the rectangle (where a originates) to one of the corners of the rectangle, where our lateral edge begins. To find the base (which we'll call b), we look at the 2x4 rectangle that forms the base of the pyramid. Now, we know the height (which we'll assign the variable a) of that triangle (1 unit) but we are not given the length of the base of the triangle. What we are looking for is the lateral edge of the pyramid, which basically amounts to a diagonal 'slice' of the pyramid. In this particular scenario, the pythagorean theorem is used twice, once to find the base and once to find the actual length we are looking for. What I find helpful is breaking the prism into two dimensional shapes.

Trapezoid prism volume khan academy