Find the surface area of the solid. Round to the nearest whole unit, if necessary: a square pyramid with a base area of 9ft^2 and a slant height of 8 ft ?

1 Answer
Juliana
Mar 5, 2018

The total surface area is #57ft^2#.

Explanation:

Imagine you have a net of the square pyramid, it should include a square at the center and 4 congruent triangles attached. enter image source here
We know that the area of the square is #9ft^2#. The area of the square could be calculated as #s^2# => #s^2=9# => #s=3#ft
We also know that the slant height is #8#ft, let's label that on our diagram.
enter image source here

The area of a triangle can be calculated as #((base)(height))/2# => #((3)(8))/2# => #12#.
We have four copies of the triangle, so we have to multiply it by 4 => #(12)(4)=48#.
Let's label all of the areas we know on our diagram now. Don't forget to label the square.
enter image source here
Looking at the diagram, we now have all we need to find the total surface area. Adding up all of the areas on the diagram we have:
#48+9=57# => #57ft^2#

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