How do you find the surface area of a pyramid with only the slant height and height?

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Jake -In order to find the surface area of a square pyramid you will need to find the length of the base s.  Look at the picture below and you will see that the slant height and the height form a right triangle with the bottom leg of the triangle equal to 1/2 s.  Use the  Pythagorean Theorem to solve for the length of the bottom leg, then solve for s.The surface area is:SA = s²  +  2 × s × l Hope that helps

think about right triangle with the slant height and height you form a right triangle. slant height=hypotenuse and height=leg so find the other leg which is HALF of one side of the base and then whatever the lenght of the other leg is just multiply by 2 in a square pyramid. for example say the slant height is 13 and the height is 12 meaning the length of the other leg is 5 so the length of one side of the base is 5x2 or 10 now with the side of the base and the slant height you can calculate the SA of each triangle in the pyramid. then calculate the base of the bottom via s^2. then add up the SA of the 4 triangles and one square in pyramid to get entire SA. in my example it would be 360 un^2 because the area is 100 and each triangle is 10x13/2or 65 but since there are 4 triangles multiply out by 4 and get 260 for area of all triangles then add up the base of 100 and get 360 un^2.