Calculate Octagonal Gazebo Dimensions

Video Transcript

"Hi! Welcome back to Expert Village. My name is Charlie Folkman and today we are going to continue building our gazebo. Now to calculate the area of our gazebo, what we are going to do is we are going to make eight points; 1, 2, 3, 4, 5, 6, 7 and 8. Now we are going to go ahead and connect these points. We are going to connect 1 and 6, 2 and 5, 3 and 8, 4 and 7. What this does for us right here is it gives us a f45 degree angle and a 90 degree angle. If we add those 2 together, we get a 145 degree angle. Now the roof is going to also have the same area. Now to calculate the square footage of our area, we are going to use two basic formulas. The first one is length x width will give us our square footage and to calculate the square footage of a triangle, we use length x width divided by 2. Now how we are going to incorporate this is we are going to go ahead and start with our middle square. Now we know that these are each foot, so we have 1, 2. So our length is going to be 2 and our width is going to be 2. So we will take that 2 x 2 following this formula equals 4 square feet. Now to get our right triangle, what we are going to have to do is turn it into a square and we will incorporate the same thing. The length is 2 and the width is 2. We will multiply those together. Two times 2 equals 4 and then we will divide that by 2 which will give us 2. Now what we are going to do with our squares is there is 1, 2, 3, 4, 5 squares so we are going to take that 4 and multiply that by 5 which will give us 20. Now we know there are 1, 2, 3, 4 right triangles and they are each 2 square feet so we are going to take that 2 and multiply it by 4 which will give us 8. Then we will go ahead and add a 20 and 8 to give us 28 total square feet. "