What`s the surface area formula for a rectangular pyramid?

##SA=lw+lsqrt(h^2+(w/2)^2)+wsqrt(h^2+(l/2)^2)##
The surface area will be the sum of the rectangular base and the ##4## triangles in which there are ##2## pairs of congruent triangles.
Area of the Rectangular Base
The base simply has an area of ##lw## since it’s a rectangle.
##=>lw##
Area of Front and Back Triangles
The area of a triangle is found through the formula ##A=1/2bh##.
Here the base is ##l##. To find the height of the triangle we must find the slant height on that side of the triangle.
The slant height can be found through solving for the hypotenuse of a right triangle on the interior of the pyramid.
The two bases of the triangle will be the height of the pyramid ##h## and one half the width ##w/2##. Through the we can see that the slant height is equal to ##sqrt(h^2+(w/2)^2)##.
This is the height of the triangular face. Thus the area of front triangle is ##1/2lsqrt(h^2+(w/2)^2)##. Since the back triangle is congruent to the front their combined area is twice the previous expression or
##=>lsqrt(h^2+(w/2)^2)##
Area of the Side Triangles
The side triangles’ area can be found in a way very similar to that of the front and back triangles except for that their slant height is ##sqrt(h^2+(l/2)^2)##. Thus the area of one of the triangles is ##1/2wsqrt(h^2+(l/2)^2)## and both the triangles combined is
##=>wsqrt(h^2+(l/2)^2)##
Total Surface Area
Simply add all of the areas of the faces.
##SA=lw+lsqrt(h^2+(w/2)^2)+wsqrt(h^2+(l/2)^2)##
This is not a formula you should ever attempt to memorize. Rather this an exercise of truly understanding the geometry of the triangular prism (as well as a bit of algebra).