How to find the surface area of a pyramid with slant height

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The surface area of any pyramid can be found by adding the surface area of the base to the surface area of the lateral faces. When working with regular pyramids, you can find the surface area using a formula, as long as you know how to find the area of the base of the pyramid. Since the base can be any polygon, it is helpful to know how to find the area of shapes such as pentagons and hexagons. When working with the common, regular square pyramid, however, calculating the total surface area is a simple calculation, provided you know the slant height of the pyramid and the side length of the square base.

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   Plug the perimeter of the base into the formula. If you aren’t given the perimeter but know the length of one edge of the base, you can calculate the perimeter by multiplying the length of one edge by the number of edges.

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   Plug the value of the slant height into the formula. Make sure you are using the slant height, not the perpendicular height. The problem should provide the slant height. If you don’t know the slant height, you cannot use this method.

   • For example, if the slant height of a hexagonal pyramid is 12 cm, your formula will look like this: .

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   Calculate the area of the base. How you do this will depend on the shape of the base. To learn more about finding the area of a polygon, read Find the Area of Regular Polygons.

   EXPERT TIP

   Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University.

   

   Grace Imson, MA
   Math Instructor, City College of San Francisco

   Our Expert Agrees: The surface area of a pyramid is equal to the sum of the areas of all of the faces. First, you have to get the area of the base, then add the area of the lateral sides, which is one face times the number of sides.

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   Plug the area of the base into the formula. Make sure you substitute for the variable .

   • For example, if the area of the hexagonal base is 41.57 sq. cm., your formula for surface area will now look like this: .

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   Multiply the perimeter of the base and the slant height of the pyramid. Then, divide by two. This will give you the lateral surface area of the pyramid.

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   Add the two values together. The sum will be the lateral surface area, plus the base surface area, providing you with the total surface area for the pyramid, in square units.

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   Square the side length of the base. This will give you the surface area of the base.

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   Multiply the side length of the base by the slant height and divide by two. Then, multiply by 4. This will give you the lateral surface area of the pyramid.

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   Add the base surface area and the lateral surface area. This will give you the total surface area of the pyramid, in square units.

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Add New Question

• Question

  How do you find the lateral area of hexagonal pyramid, given the height and length of each side?

  

  Use the base times height for the rectangles, and the altitude times base of the hexagonal face times three.

• Question

  How would you calculate the surface area of pyramid that does not have a square base?

  

  Use the formula (p x h/2) + (B), where p is the perimeter of the base, h is the slant height of the pyramid, and B is the area of the base. Below are some articles on finding the area of a pentagon and hexagon, two common pyramid bases: http://www.wikihow.com/Find-the-Area-of-a-Pentagon http://www.wikihow.com/Calculate-the-Area-of-a-Hexagon

• Question

  How do I double the lateral surface area of a square pyramid?

  

  One way would be to double either the length of the sides of the base or the slant height (but not both).

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Article SummaryX

To find the surface area of a pyramid, start by multiplying the perimeter of the pyramid by its slant height. Then, divide that number by 2. Finally, add the number you get to the area of the pyramid's base to find the surface area. To learn how to find the surface area of a square pyramid, scroll down!

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