Kay so we had this problem today that we're sposed to do tonight. Goes something like this:
There's a pyramid 150m tall, with a square base. Each side of the base is 230m. Find the area of the horizontal cross section 50m above the base, using 3 different methods.
So first off, I did a right triangle to get the height of one of the 4 triangles forming the pyramid. So the triangle would have a base of 115 m, and the height would be 150. Pythagorean theorem says the hypotenuse is 189 .
Then I cut off a part of the triangle at the 50m mark, and form another triangle with that, so I have two right triangles and a rectangle. I need to find the length of the rectangle to get the area of the horizontal cross section 50m up. So I use sin on the original triangle to get the base angle, which turns out to be 52.53. We also know that the height of the newly formed base triangle is 50 because that's where I need to find the horizontal cross section.
So I use the sin function again and find out that the base of that triangle is 38.33m. Subtract that from the original base of 115m, and I get about 76.67. Now I have to remember that this is only half of the length of the horizontal cross section, so I multiply that by two, then use the area of a square formula and get the answer, which happens to be around 23, 515m^2.
Now this is great and all, but the question requires me to solve this using 3 different methods. So I'm looking for helping figuring out what the other two methods are. Thanks! =D