If the given figure was folded into a square pyramid, determine its lateral surface area.
So if we would fold this to become a square pyramid, we will need to take each of these vertices and bring them together to create a point. So it would look something like this. So the lateral surface area will be the area of all of the sides except for the base. And the base is a square. And we’re told the lengths of the sides of the square are 14. And the height of the triangles are 15. So we do not need the base of the square.
So we need to add up the area of all four triangles. And since all four triangles are the same, we can find the area of one of the triangles and multiply it by four. So again, to find the lateral surface area, we will take the area of a triangle and then multiply it by four. And the area of a triangle is one half base times height. So the base of the triangle will be 14, where the height of the triangle will be 15.
So let’s first multiply one half times 14 times 15. And we get 105. And 105 times four is 420. Since our units are in centimeters and it’s an area, it should be 420 centimeters squared. Therefore, the lateral area, meaning all of the surface area except for the base, the bottom, it will be 420 square centimeters.