How to Find the Surface Area of a Pentagon


Hi, I'm Charlie Kasov and this is is how to find the surface area of a pentagon. Now, to find the surface area or area of a pentagon, the formula is five over two times s times a; where s is side, a is apotheum, which is basically the radius of a polygon. So, similar to a circle but it's for a polygon. So, if we have a pentagon, which usually looks like a house; now keep in mind this is the formula for a regular pentagon, the side would be the same for all five, the apotheum would be the same for all five sides. So, let's say side equals four, it doesn't matter what measurement we're using, the number is what we multiply, and the apotheum will say equals three. So, four over here and then from center to the middle of one side would be the apotheum, that would be three. So, you do five over two times four times three. So, five over two times four times three; four times three is 12, times five over two. Now, a nice trick for multiplying five over two if you're intimidated, just focus on the top or the bottom. If we focus on the top, we multiply, so 12 times five is 60, divided by two is 30. You could also do 12 divided by two, which is six and then multiply by five which is 30. So, that is how you find the surface are of the pentagon.

Charlie Kasov has been tutoring high school mathematics since 2004. He is qualified to teach several math subjects, including geometry, algebra, trigonometry and probability.