Question

A square pyramid has a slant height of 13 meters and a height of 12 meters. What is the surface area if the square base has sides of length 10 meters?

Answer 1

as you can see, you have a square at the bottom
with 4 triangles standing above the square and touching each other
so it's really the Area of the square PLUS the Area of the triangles

the square base, is peanuts, is just a square, so its Area will be 10x10, length x width

Answer 2

the are of a triangle is just 1/2 x base x height

as you can see in the picture
the so-called "slant height" is really the "nose of the face of the triangle", or it's height
and is 13

so the Area of one of those triangles will be 1/2 x ( 10 ) x ( 13 )

you have 4 triangles with the same area, you add their area
PLUS the square base
and that'd be the total surface area