Math Tip of the Day: Surface Area Part 2

Last week’s math tip was on surface area.  We looked at the two different types of surface area:  lateral and total.  We also provided tips on calculating surface area correctly.  Remember that the formula for total surface area also includes the formula for the lateral surface area.  This makes it easier to calculate.

 Last week’s post focused on prisms and cylinders.  Today we will look at calculating surface area for cones and pyramids.  Both cones and pyramids have a slant height.  The slant height is represented with the variable l.  Please do not confuse this with length for cones and pyramids.  Slant height is different from the height of these shapes.  The height extends from the vertex to the base, whereas the slant height is just that, the slanted height of the shape (see examples below).  Sometimes the slant height is not given, but can be found by using the Pythagorean Theorem or Trigonometry.  
 
Let’s look at some examples:
 
 
The base of a cone is always the shape of a circle.

 

The base of a pyramid can be one of several shapes.  Rectangle, square, triangle or a polygon such as a hexagon.  Do not forget to take 1/2 when calculating, since it is part of the formula.
**Remember P = Perimeter of the base and B = area of the base.  l = slant height, not length.
What challenges do you face when calculating surface area?