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

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#### Explanation

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The surface area will be the sum of the rectangular base and the

**Area of the Rectangular Base**

The base simply has an area of

#=>lw#

**Area of Front and Back Triangles**

The area of a triangle is found through the formula

Here, the base is *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,

This is the height of the triangular face. Thus, the area of front triangle is

#=>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

#=>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).

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