This image shows a square pyramid. what is the surface area of this square pyramid?
25 ft²
100 ft²
125 ft²
200 ft²
note: image not drawn to scale. the figure shows a square pyramid. the slant height is shown as a dashed line perpendicular to the base edge. the length of the base edge is 10 feet. the lateral edge makes a 45 degree angle with the base edge.

  200 ft²

Step-by-step explanation:

Each face is an isosceles right triangle with a hypotenuse of length 10 ft. The area of each of those triangles is

  A = 1/4·h² . . . . where the h in this formula is the hypotenuse length

So, the area of the four faces (the lateral area of the pyramid is 4 times this, or ...

  A = 4·1/4·(10 ft)² = 100 ft²

Of course, the base area is simply the area of the square base, the square of its side length:

  A = (10 ft)² = 100 ft²

So, the total area is the sum of the lateral area and the base area:

  total area = 100 ft² +100 ft² = 200 ft²

If you think about this for a little bit, you will realize the pyramid must have zero height. That is, the slant height of a face is exactly the same as the distance from the center of an edge to the center of the base. "Not drawn to scale" is a good description.

395.84

step-by-step explanation:

2πrh+2πr²

2 (pie)(radius)(height)+2(pie)(radius)^2