How to Get the Lateral Area of a Pentagonal Pyramid

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Getting the lateral area of a pentagonal pyramid is something that you need to do while paying close attention to the base. Get the lateral area of a pentagonal pyramid with help from an experienced mathematics educator in this free video clip.

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Video Transcript

Hello, my name is Walter Unglaub. And this is how to get the lateral are of a pentagonal pyramid. So, here I have a 3-D view of a pentagonal pyramid. In which the base of this regular pyramid is a pentagon as viewed from the top. And I have a length A at the base of each of these triangles. So, I have A at every base. And from a side view, I can see that the pyramid has some height, H. And it also has a slant height, which I'm going to denote as capital H sub S. And this is the length of this hypotenuse. So, the general formula for the lateral area of a pyramid is A sub L for area lateral is equal to one-half times the perimeter of base times the slant height. Which is capital H sub S. Now, the perimeter of the base is easy to calculate here. It's simply going to be the value A multiplied by five. Since there are five bases. So, the base of the entire pyramid then, PB is equal to five-A. Now the formula for the slant height depends on how many faces the pyramid has. In the case of a pentagonal pyramid, it's given by the following equation. A slant height is equal to the square root of H-squared plus 120th times five plus two times the square root of five, times A-squared. So, this is a complicated looking equation. But the point is, if we know what the value of A is and the value of this height of the pyramid is. Then, we can in principle compute the equation for the lateral area. So, given the values A is equal to one meter and H is also equal to one meter. Let's call this parameter set P.. If you want to evaluate PB at the parameter set P, we get five times one meters. And that's simply equal to five meters for the perimeter of the base. And then, for the slant height, we get one point two one four meters approximately. Therefore, we can compute the lateral area as one-half times the perimeter of the base, which is five meters times the slant height which one point two one four meters. And this is approximately equal to three point zero three five meters squared. So, by following this general formula and arriving the slant height as a function of the height H and the base A for one of the sides. One can relatively, easily calculate the lateral area. My name is Walter Unglaub, and this is how to get the lateral are of a pentagonal pyramid.


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